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Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850069
We construct three families of vertex algebras along with their modules from appropriate vertex Lie algebras, using the constructions in [Vertex Lie algebra,... 
Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650009
We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded... 
Logarithmic intertwining operators | Strongly graded vertex algebra | cofiniteness condition | Differential equations | Logarithmic tensor category | MATHEMATICS | logarithmic tensor category | MATHEMATICS, APPLIED | logarithmic intertwining operators | C-1-cofiniteness condition | differential equations | Algebra
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 05/2016, Volume 27, Issue 5, p. 1650046
We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along... 
strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 8/2015, Volume 337, Issue 3, pp. 1053 - 1076
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type... 
Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ALGEBRAS | VERTEX REPRESENTATIONS | PHYSICS, MATHEMATICAL | CATEGORIFICATION | Algebra
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 06/2008, Volume 41, Issue 25, p. 255204
The centrally extended superalgebra psu(2 vertical bar 2) x R-3 was shown to play an important role for the integrable structures of the one-dimensional... 
DILATATION OPERATOR | INTEGRABLE SPIN CHAIN | VERTEX MODEL | T-J MODELS | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | ALGEBRAIC BETHE-ANSATZ | STRONGLY CORRELATED ELECTRONS | EXACTLY SOLVABLE MODEL | LIE SUPERALGEBRA GL(2/2) | PHYSICS, MATHEMATICAL | GAUGE
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 09/2014, Volume 886, Issue C, pp. 436 - 482
Journal Article
Transformation Groups, ISSN 1083-4362, 12/2017, Volume 22, Issue 4, pp. 1005 - 1029
We investigate the representation theory of domestic group schemes G $$ \mathcal{G} $$ over an algebraically closed field of characteristic p > 2. We present... 
Topological Groups, Lie Groups | Mathematics | Algebra | LIE-ALGEBRAS | MATHEMATICS | QUIVERS | PRODUCTS | STRONGLY GRADED RINGS | HOPF GALOIS EXTENSIONS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 07/2008, Volume 41, Issue 29, p. 295202
We present in a unified and detailed way the nested Bethe ansatz for closed spin chains based on Y(gl (n)), Y(gl (m|n)), (U) over cap (q)(gl (n)) or (U) over... 
ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | ALGEBRA | TRANSFER-MATRICES | EQUATIONS | FINITE-DIMENSIONAL REPRESENTATIONS | MODEL | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS
Journal Article
Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 07/2013, Volume 2013, Issue 7, pp. P07009 - 19
The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer... 
integrable spin chains (vertex models) | solvable lattice models | quantum integrability (Bethe ansatz) | MECHANICS | XXZ SPIN CHAIN | OPERATOR | T-J MODEL | PHYSICS, MATHEMATICAL | EQUATION | Hierarchies | Mathematical analysis | Transfer matrices | Eigenvalues | Mathematical models | Spectra | Boundaries | Polarons
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 1998, Volume 516, Issue 3, pp. 588 - 602
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is... 
QUANTUM SUPERSYMMETRY | SUPERCONDUCTIVITY | ALGEBRAIC BETHE-ANSATZ | MATRICES | VERTEX | EXACTLY SOLVABLE MODEL | SYSTEMS | OPEN SPIN CHAINS | PHYSICS, PARTICLES & FIELDS
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 2004, Volume 687, Issue 3, pp. 257 - 278
We formulate the Bethe ansatz equations for the open super-spin chain based on the super Yangian of osp( M|2 n) and with diagonal boundary conditions. We then... 
SYMMETRY | FUSION | MASSIVE THIRRING MODEL | QUANTUM-SYSTEMS | T-J MODEL | PHYSICS, NUCLEAR | INTEGRABLE MODEL | SPECTRUM | SUPERSYMMETRIC U MODEL | OPEN-BOUNDARY CONDITIONS | PHYSICS, PARTICLES & FIELDS | Quantum Algebra | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 05/2006, Volume 264, Issue 1, pp. 87 - 114
We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and... 
CHAIN | EXACTLY SOLVABLE MODEL | PHYSICS, MATHEMATICAL | CORRELATED ELECTRONS
Journal Article
Mathematical Notes, ISSN 0001-4346, 12/2009, Volume 86, Issue 5, pp. 665 - 681
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 05/2009, Volume 42, Issue 20, pp. 205203 - 205203 (35)
We present in a unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(n)), Y(gl(m|n)), (U) over cap (q)(gl(n)) or (U) over cap... 
REPRESENTATIONS | ANALOG | PHYSICS, MULTIDISCIPLINARY | QUANTUM | TRANSFER-MATRICES | VERTEX | SPECTRUM | MODEL | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics | Physics
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2007, Volume 48, Issue 2, pp. 023504 - 023504-12
By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the g l ( 1 ∣ 1 ) and g l ( 2 ∣ 1 ) supersymmetric... 
T-J MODEL | 6-VERTEX MODEL | PHYSICS, MATHEMATICAL | ALGEBRAIC BETHE-ANSATZ | MATRIX MODEL | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERSYMMETRY | PARTITION FUNCTIONS | LIE GROUPS | DOMAIN STRUCTURE | BOUNDARY CONDITIONS
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 1/2018, Volume 357, Issue 1, pp. 295 - 317
We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley–Lieb algebra) does... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MODELS | PHYSICS, MATHEMATICAL | Algebra
Journal Article
Communications in Algebra, ISSN 0092-7872, 12/2019, Volume 47, Issue 12, pp. 5303 - 5316
We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and... 
stretching operator | strongly stable ideals | Alexander dual | generic initial ideals | Betti numbers
Journal Article
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