European Journal of Combinatorics, ISSN 0195-6698, 10/2018, Volume 73, pp. 89 - 113

Factorial characters of each of the classical Lie groups have recently been defined algebraically as rather simple deformations of irreducible characters. Each...

MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | DEFORMATIONS | PATHS | FORMULAS | ALTERNATING SIGN MATRICES | CHARACTERS

MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | DEFORMATIONS | PATHS | FORMULAS | ALTERNATING SIGN MATRICES | CHARACTERS

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2015, Volume 131, pp. 1 - 31

Half-turn symmetric alternating sign matrices (HTSASMs) are special variations of the well-known alternating sign matrices which have a long and fascinating...

Weyl's denominator formula | Alternating sign matrices | Shifted tableaux | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | IDENTITIES | DEFORMATIONS | PATHS | WEYLS DENOMINATOR FORMULA | ENUMERATION | PLANE PARTITIONS | ODD ORDER

Weyl's denominator formula | Alternating sign matrices | Shifted tableaux | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | IDENTITIES | DEFORMATIONS | PATHS | WEYLS DENOMINATOR FORMULA | ENUMERATION | PLANE PARTITIONS | ODD ORDER

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 11/2002, Volume 16, Issue 3, pp. 269 - 300

A determinantal expansion due to Okada is used to derive both a deformation of Weyl's denominator formula for the Lie algebra sp(2n) of the symplectic group...

Convex and Discrete Geometry | alternating sign matrices | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Weyl's denominator formula | symplectic shifted tableau | monotone triangle | Monotone triangle | Symplectic shifted tableau | Alternating sign matrices | MATHEMATICS | PLANE PARTITIONS | CHARACTERS | Algebra

Convex and Discrete Geometry | alternating sign matrices | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Weyl's denominator formula | symplectic shifted tableau | monotone triangle | Monotone triangle | Symplectic shifted tableau | Alternating sign matrices | MATHEMATICS | PLANE PARTITIONS | CHARACTERS | Algebra

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 6/2005, Volume 21, Issue 4, pp. 395 - 421

Alternating sign matrices with a U-turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of...

Convex and Discrete Geometry | alternating sign matrices | symplectic tableaux | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Symplectic tableaux | Alternating sign matrices | MATHEMATICS | FORMULA | CLASSICAL LIE-GROUPS | DEFORMATIONS | Computer science

Convex and Discrete Geometry | alternating sign matrices | symplectic tableaux | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Symplectic tableaux | Alternating sign matrices | MATHEMATICS | FORMULA | CLASSICAL LIE-GROUPS | DEFORMATIONS | Computer science

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 05/2018, Volume 59, Issue 5, p. 53505

We present a method to analyze the wavefunctions of six-vertex models by extending the Izergin–Korepin analysis originally developed for domain wall boundary...

SYMPLECTIC SHIFTED TABLEAUX | XYZ-SPIN | REFINED CAUCHY/LITTLEWOOD IDENTITIES | DEFORMATIONS | SPIN CHAIN | ALTERNATING-SIGN MATRICES | VERTEX MODELS | PHYSICS, MATHEMATICAL | PLANE PARTITIONS | BETHE-ANSATZ | SOS MODEL

SYMPLECTIC SHIFTED TABLEAUX | XYZ-SPIN | REFINED CAUCHY/LITTLEWOOD IDENTITIES | DEFORMATIONS | SPIN CHAIN | ALTERNATING-SIGN MATRICES | VERTEX MODELS | PHYSICS, MATHEMATICAL | PLANE PARTITIONS | BETHE-ANSATZ | SOS MODEL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 4/2019, Volume 109, Issue 4, pp. 923 - 943

We introduce and study a class of partition functions of an elliptic free-fermionic face model. We study the partition functions with a triangular boundary...

16T30 | 82B23 | Theoretical, Mathematical and Computational Physics | Complex Systems | 33E05 | Physics | Geometry | Elliptic Pfaffians | Yang-Baxter equation | Partition functions | Group Theory and Generalizations | Elliptic integrable models | 16T25 | SYMMETRY CLASSES | 6-VERTEX MODEL | FORMULA | PHYSICS, MATHEMATICAL | SOS MODEL | SCALAR PRODUCTS | SYMPLECTIC SHIFTED TABLEAUX | XYZ-SPIN | DEFORMATIONS | ALTERNATING-SIGN MATRICES | VERTEX MODELS | Operating systems | Analysis | Models

16T30 | 82B23 | Theoretical, Mathematical and Computational Physics | Complex Systems | 33E05 | Physics | Geometry | Elliptic Pfaffians | Yang-Baxter equation | Partition functions | Group Theory and Generalizations | Elliptic integrable models | 16T25 | SYMMETRY CLASSES | 6-VERTEX MODEL | FORMULA | PHYSICS, MATHEMATICAL | SOS MODEL | SCALAR PRODUCTS | SYMPLECTIC SHIFTED TABLEAUX | XYZ-SPIN | DEFORMATIONS | ALTERNATING-SIGN MATRICES | VERTEX MODELS | Operating systems | Analysis | Models

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2018, Volume 134, pp. 58 - 76

We analyze the scalar products of the elliptic Felderhof model introduced by Foda–Wheeler–Zuparic as an elliptic extension of the trigonometric face-type...

Representation theory | Partition functions | Elliptic integrable models | Symmetric functions | LIE-SUPERALGEBRAS | SOS MODELS | 6-VERTEX MODEL | PHYSICS, MATHEMATICAL | PLANE PARTITIONS | ALTERNATING SIGN MATRICES | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | REFINED CAUCHY/LITTLEWOOD IDENTITIES | DEFORMATIONS | VERTEX MODELS | IRF MODELS

Representation theory | Partition functions | Elliptic integrable models | Symmetric functions | LIE-SUPERALGEBRAS | SOS MODELS | 6-VERTEX MODEL | PHYSICS, MATHEMATICAL | PLANE PARTITIONS | ALTERNATING SIGN MATRICES | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | REFINED CAUCHY/LITTLEWOOD IDENTITIES | DEFORMATIONS | VERTEX MODELS | IRF MODELS

Journal Article

Annals of Mathematics, ISSN 0003-486X, 7/2007, Volume 166, Issue 1, pp. 293 - 316

"Weyl group multiple Dirichlet series" were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta,...

Integers | Series convergence | Algebra | Root systems | Whittaker functions | Polynomials | Matrices | Coefficients | Tableaux | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | FORMULAS | DEFORMATIONS | ALTERNATING SIGN MATRICES | CHARACTERS

Integers | Series convergence | Algebra | Root systems | Whittaker functions | Polynomials | Matrices | Coefficients | Tableaux | MATHEMATICS | SYMPLECTIC SHIFTED TABLEAUX | FORMULAS | DEFORMATIONS | ALTERNATING SIGN MATRICES | CHARACTERS

Journal Article

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, ISSN 2050-3911, 12/2017, Volume 2017, Issue 12

We investigate the elliptic integrable model introduced by Deguchi and Martin [Int. J. Mod. Phys. A 7, Suppl. 1A, 165 (1992)], which is an elliptic extension...

SYMPLECTIC SHIFTED TABLEAUX | PHYSICS, MULTIDISCIPLINARY | DEFORMATIONS | VERTEX MODELS | FORMULAS | ALTERNATING SIGN MATRICES | SOS MODEL | PHYSICS, PARTICLES & FIELDS

SYMPLECTIC SHIFTED TABLEAUX | PHYSICS, MULTIDISCIPLINARY | DEFORMATIONS | VERTEX MODELS | FORMULAS | ALTERNATING SIGN MATRICES | SOS MODEL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/1998, Volume 209, Issue 1, pp. 1 - 64

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All...

plane partitions | Littlewood–Richardson rule | tableaux | Schur functions | symplectic characters | general linear characters | characters of Lie groups | restriction rules | orthogonal characters | Littlewood-Richardson rule | General linear characters | Characters of Lie groups | Symplectic characters | Orthogonal characters | Tableaux | Restriction rules | Plane partitions | SHIFTED PLANE PARTITIONS | REPRESENTATIONS | INVARIANT-THEORY | MATHEMATICS | LIE-GROUPS | YOUNG-DIAGRAMMATIC METHODS | BRANCHING-RULES | SYMPLECTIC GROUPS

plane partitions | Littlewood–Richardson rule | tableaux | Schur functions | symplectic characters | general linear characters | characters of Lie groups | restriction rules | orthogonal characters | Littlewood-Richardson rule | General linear characters | Characters of Lie groups | Symplectic characters | Orthogonal characters | Tableaux | Restriction rules | Plane partitions | SHIFTED PLANE PARTITIONS | REPRESENTATIONS | INVARIANT-THEORY | MATHEMATICS | LIE-GROUPS | YOUNG-DIAGRAMMATIC METHODS | BRANCHING-RULES | SYMPLECTIC GROUPS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/1983, Volume 89, Issue 3, pp. 553 - 559

The number of shifted plane partitions contained in the shifted shape [ p + q - 1, p + q - 3,..., p - q + 1 ] with part size bounded by m is shown to be equal...

Integers | Mathematical theorems | Algebra | Cardinality | Interval partitions | Geometric planes | Partially ordered sets | Polynomials | Tableaux | Physics | Zeta polynomials | Young tableaux | Representations of symplectic Lie algebras | Plane partitions

Integers | Mathematical theorems | Algebra | Cardinality | Interval partitions | Geometric planes | Partially ordered sets | Polynomials | Tableaux | Physics | Zeta polynomials | Young tableaux | Representations of symplectic Lie algebras | Plane partitions

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2011, Volume 25, Issue 2, pp. 539 - 560

We provide a combinatorial proof of a symplectic character identity relating the sum of a product of symplectic Schur functions to the product Pi(m)(i-1)...

Dual pair identities | Schur functions | Symplectic tableaux | Jeu de taquin | MATHEMATICS, APPLIED | REPRESENTATIONS | dual pair identities | symplectic tableaux | SPINORS | jeu de taquin

Dual pair identities | Schur functions | Symplectic tableaux | Jeu de taquin | MATHEMATICS, APPLIED | REPRESENTATIONS | dual pair identities | symplectic tableaux | SPINORS | jeu de taquin

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2012, Volume 53, Issue 10, p. 103502

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed...

TOEPLITZ | GAUGE-THEORY | CHERN-SIMONS-THEORY | 2-DIMENSIONAL QCD | CRYSTAL | SEIBERG-WITTEN THEORY | CALABI-YAU | 2D YANG-MILLS | PHYSICS, MATHEMATICAL | BLACK-HOLES | TODA | Partitions | Hierarchies | Mathematical analysis | Constants | Mathematical models | Representations | Stochasticity | Invariants | INTEGRAL CALCULUS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | STOCHASTIC PROCESSES | SYMMETRY | M-THEORY | PARTITION FUNCTIONS | GAUGE INVARIANCE

TOEPLITZ | GAUGE-THEORY | CHERN-SIMONS-THEORY | 2-DIMENSIONAL QCD | CRYSTAL | SEIBERG-WITTEN THEORY | CALABI-YAU | 2D YANG-MILLS | PHYSICS, MATHEMATICAL | BLACK-HOLES | TODA | Partitions | Hierarchies | Mathematical analysis | Constants | Mathematical models | Representations | Stochasticity | Invariants | INTEGRAL CALCULUS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | STOCHASTIC PROCESSES | SYMMETRY | M-THEORY | PARTITION FUNCTIONS | GAUGE INVARIANCE

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 05/2004, Volume 2004, Issue 5, pp. 029 - 669

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all...

Differential and Algebraic Geometry | Sigma Models | D-branes | differential and algebraic geometry | sigma models | HOMOGENEOUS SPACES | FUSION RULES | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Differential and Algebraic Geometry | Sigma Models | D-branes | differential and algebraic geometry | sigma models | HOMOGENEOUS SPACES | FUSION RULES | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

2003, Progress in mathematics, ISBN 9783764342326, Volume 213., xii, 472

Book

Letters in Mathematical Physics, ISSN 0377-9017, 11/2015, Volume 105, Issue 11, pp. 1551 - 1586

We study lozenge tilings of a domain with partially free boundary. In particular, we consider a trapezoidal domain (half-hexagon), s.t. the horizontal lozenges...

symmetric plane partitions | 60C05 | free boundary | Theoretical, Mathematical and Computational Physics | Schur functions | Gaussian Unitary Ensemble | 60B20 | 82B20 | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | limit shape | 05E05 | symplectic characters | GUE-corners process | Group Theory and Generalizations | lozenge tilings | 05A15 | 60F05 | PHYSICS, MATHEMATICAL

symmetric plane partitions | 60C05 | free boundary | Theoretical, Mathematical and Computational Physics | Schur functions | Gaussian Unitary Ensemble | 60B20 | 82B20 | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | limit shape | 05E05 | symplectic characters | GUE-corners process | Group Theory and Generalizations | lozenge tilings | 05A15 | 60F05 | PHYSICS, MATHEMATICAL

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 12/2009, Volume 26, Issue 23, pp. 235023 - 235023 (31)

A two-parameter group element is presented that interpolates between M-brane solutions. The group element is used to interpret a number of exotic branes...

Physics - High Energy Physics - Theory

Physics - High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 6/2012, Volume 2012, Issue 6, pp. 1 - 40

We study the Nekrasov-Shatashvili limit of the $ \mathcal{N} $ = 2 supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau...

Topological Strings | Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Topological strings | DUALITY | N=2 | PHYSICS, PARTICLES & FIELDS | Analysis | Universities and colleges

Topological Strings | Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Topological strings | DUALITY | N=2 | PHYSICS, PARTICLES & FIELDS | Analysis | Universities and colleges

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 1/2013, Volume 2013, Issue 1, pp. 1 - 20

We derive Seiberg-Witten like equations encoding the dynamics of $ \mathcal{N}=2 $ ADE quiver gauge theories in presence of a non-trivial Ω-background along a...

Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Nonperturbative Effects | Elementary Particles, Quantum Field Theory | GAUGE-THEORIES | ONE-INSTANTON PREDICTIONS | REPRESENTATION | DUALITY | BRANES | SU(N) | MONOPOLES | HYPERMULTIPLETS | PHYSICS, PARTICLES & FIELDS | Gauge theory | Deformation | Planes | Dynamics | Mathematical analysis | Correlators | Two dimensional | Physics - High Energy Physics - Theory

Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Nonperturbative Effects | Elementary Particles, Quantum Field Theory | GAUGE-THEORIES | ONE-INSTANTON PREDICTIONS | REPRESENTATION | DUALITY | BRANES | SU(N) | MONOPOLES | HYPERMULTIPLETS | PHYSICS, PARTICLES & FIELDS | Gauge theory | Deformation | Planes | Dynamics | Mathematical analysis | Correlators | Two dimensional | Physics - High Energy Physics - Theory

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 03/2005, Volume 254, Issue 2, pp. 425 - 478

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology...

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Physics | Statistical Physics | FIELD-THEORY | STRING AMPLITUDES | DUALITY | KNOT | LINK INVARIANTS | PHYSICS, MATHEMATICAL | GRAVITY

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Physics | Statistical Physics | FIELD-THEORY | STRING AMPLITUDES | DUALITY | KNOT | LINK INVARIANTS | PHYSICS, MATHEMATICAL | GRAVITY

Journal Article

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