Mathematische Annalen, ISSN 0025-5831, 4/2018, Volume 370, Issue 3, pp. 1805 - 1881

...) . As an application, we deduce the existence of a natural set of periods attached to cuspidal automorphic representations of $${{\mathrm{\mathrm {GL}}}(n)$$ GL(n...

Mathematics, general | Mathematics | MATHEMATICS | UNITARY REPRESENTATIONS | LIE-GROUPS | ALGEBRA | HARISH-CHANDRA MODULES | ARITHMETIC GROUPS | EISENSTEIN COHOMOLOGY

Mathematics, general | Mathematics | MATHEMATICS | UNITARY REPRESENTATIONS | LIE-GROUPS | ALGEBRA | HARISH-CHANDRA MODULES | ARITHMETIC GROUPS | EISENSTEIN COHOMOLOGY

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2018, Volume 51, Issue 2, p. 25207

An eigenfunction method is applied to reduce the regular projective representations (Reps...

Class operator | Anti-unitary group | Projective representations | Eigenfunction method | class operator | projective representations | STATES | PHYSICS, MULTIDISCIPLINARY | FINITE-GROUPS | NONUNITARY GROUPS | PHYSICS, MATHEMATICAL | anti-unitary group | eigenfunction method

Class operator | Anti-unitary group | Projective representations | Eigenfunction method | class operator | projective representations | STATES | PHYSICS, MULTIDISCIPLINARY | FINITE-GROUPS | NONUNITARY GROUPS | PHYSICS, MATHEMATICAL | anti-unitary group | eigenfunction method

Journal Article

Journal of computational chemistry, ISSN 1096-987X, 2019, Volume 41, Issue 2, pp. 129 - 135

The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach...

unitary group approach | GUGA | graphical unitary group approach | Shavitt graph | UGA

unitary group approach | GUGA | graphical unitary group approach | Shavitt graph | UGA

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 11/2010, Volume 7, Issue 7, pp. 1191 - 1306

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the...

projective space | script T sign-symmetry | quasi-Hermitian | unitary-equivalence | biorthonormal system | metric operator | observable | complex potential | Pseudo-Hermitian | quantization | COMPLEX TRAJECTORIES | GENERALIZED PT-SYMMETRY | PT-symmetry | PHYSICAL REALIZATION | KLEIN-GORDON FIELDS | PHYSICS, MATHEMATICAL | CLASSICAL TRAJECTORIES | PERTURBATION-THEORY | HAMILTONIANS | HILBERT-SPACE | OPERATORS | QUASI-HERMITICITY

projective space | script T sign-symmetry | quasi-Hermitian | unitary-equivalence | biorthonormal system | metric operator | observable | complex potential | Pseudo-Hermitian | quantization | COMPLEX TRAJECTORIES | GENERALIZED PT-SYMMETRY | PT-symmetry | PHYSICAL REALIZATION | KLEIN-GORDON FIELDS | PHYSICS, MATHEMATICAL | CLASSICAL TRAJECTORIES | PERTURBATION-THEORY | HAMILTONIANS | HILBERT-SPACE | OPERATORS | QUASI-HERMITICITY

Journal Article

5.
Full Text
Unitary irreducible representations of SL (2,C) in discrete and continuous SU (1,1) bases

Journal of mathematical physics, ISSN 1089-7658, 2011, Volume 52, Issue 1, p. 012501

We derive the matrix elements of generators of unitary irreducible representations of SL(2, C...

COMPLEX ANGULAR MOMENTA | PHYSICS, MATHEMATICAL | QUANTUM-GRAVITY | HOMOGENEOUS LORENTZ GROUP | Physics - General Relativity and Quantum Cosmology | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | LIE GROUPS | SYMMETRY GROUPS | MATRIX ELEMENTS | SL GROUPS | FUNCTIONS | IRREDUCIBLE REPRESENTATIONS | MATHEMATICAL METHODS AND COMPUTING | SU-2 GROUPS | SU GROUPS | UNITARY SYMMETRY

COMPLEX ANGULAR MOMENTA | PHYSICS, MATHEMATICAL | QUANTUM-GRAVITY | HOMOGENEOUS LORENTZ GROUP | Physics - General Relativity and Quantum Cosmology | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | LIE GROUPS | SYMMETRY GROUPS | MATRIX ELEMENTS | SL GROUPS | FUNCTIONS | IRREDUCIBLE REPRESENTATIONS | MATHEMATICAL METHODS AND COMPUTING | SU-2 GROUPS | SU GROUPS | UNITARY SYMMETRY

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 2015, Volume 206, Issue 1, pp. 1 - 38

The notion of derivatives for smooth representations of GL(n, a"e (p) ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations...

MATHEMATICS | UNITARY REPRESENTATIONS | WHITTAKER VECTORS | SERIES | HARISH-CHANDRA MODULES | VARIETIES | ADIC GROUPS | OPERATORS | ANNIHILATORS | CONJECTURE | Mathematical research | Research | Mappings (Mathematics) | Mathematics - Representation Theory

MATHEMATICS | UNITARY REPRESENTATIONS | WHITTAKER VECTORS | SERIES | HARISH-CHANDRA MODULES | VARIETIES | ADIC GROUPS | OPERATORS | ANNIHILATORS | CONJECTURE | Mathematical research | Research | Mappings (Mathematics) | Mathematics - Representation Theory

Journal Article

2017, ISBN 9783319646107, 659

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations...

Mathematics | Group Theory and Generalizations | Quantum Physics | Topological Groups, Lie Groups | Mathematical Physics | Quantum fields | Heisenberg group | Poisson bracket and symplectic geometry | Quantum free particle | Hamiltonian vector fields | Lie algebras | Quantization | Standard model of particle physics | Fermionic oscillator | Fourier analysis and free particle | Schroedinger representation | Rotation and spin groups | Unitary group representations | Metaplectic representation | Lie algebra representations | Quantum mechanics | Lie groups | Representation theory | Momentum and free particle | Two-state systems | Quantum theory | Group theory | Representations of groups

Mathematics | Group Theory and Generalizations | Quantum Physics | Topological Groups, Lie Groups | Mathematical Physics | Quantum fields | Heisenberg group | Poisson bracket and symplectic geometry | Quantum free particle | Hamiltonian vector fields | Lie algebras | Quantization | Standard model of particle physics | Fermionic oscillator | Fourier analysis and free particle | Schroedinger representation | Rotation and spin groups | Unitary group representations | Metaplectic representation | Lie algebra representations | Quantum mechanics | Lie groups | Representation theory | Momentum and free particle | Two-state systems | Quantum theory | Group theory | Representations of groups

eBook

Selecta Mathematica, ISSN 1022-1824, 3/2013, Volume 19, Issue 1, pp. 141 - 172

In this paper, we study irreducible unitary representations of $${GL_{n}(\mathbb{R})}$$ and prove a number of results...

BZ derivative | 22E47 | Associated variety | General linear group | 22E50 | Mathematics, general | Mathematics | Annihilator | Whittaker functional | Howe rank | Unitary dual | 22E46 | MATHEMATICS, APPLIED | CLASSIFICATION | IRREDUCIBLE REPRESENTATIONS | CONJECTURE | CHARACTERS | P-ADIC GROUPS | MATHEMATICS | MODULES | MODELS | VECTORS | OPERATORS

BZ derivative | 22E47 | Associated variety | General linear group | 22E50 | Mathematics, general | Mathematics | Annihilator | Whittaker functional | Howe rank | Unitary dual | 22E46 | MATHEMATICS, APPLIED | CLASSIFICATION | IRREDUCIBLE REPRESENTATIONS | CONJECTURE | CHARACTERS | P-ADIC GROUPS | MATHEMATICS | MODULES | MODELS | VECTORS | OPERATORS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2019, Volume 292, Issue 1, pp. 387 - 402

Based on an idea by Gan and Savin (Represent Theory 9:46–93, 2005), we give a classification of minimal representations of connected simple real Lie groups not of type...

22E47 | 15A72 | Mathematics, general | 20G05 | Mathematics | Minimal representation | Reductive group | 22E46 | MATHEMATICS | UNITARY REPRESENTATIONS | MODULES | ORBIT | GEOMETRIC-QUANTIZATION | O(P | REALIZATION

22E47 | 15A72 | Mathematics, general | 20G05 | Mathematics | Minimal representation | Reductive group | 22E46 | MATHEMATICS | UNITARY REPRESENTATIONS | MODULES | ORBIT | GEOMETRIC-QUANTIZATION | O(P | REALIZATION

Journal Article

Journal für die reine und angewandte Mathematik, ISSN 0075-4102, 09/2017, Volume 2017, Issue 730, pp. 1 - 64

...–Stevens, Urban, and others. We also formulate a precise modularity conjecture linking trianguline Galois representations with overconvergent cohomology classes...

MATHEMATICS | FIELDS | UNITARY GROUPS | SPACES | FAMILIES | ARITHMETIC GROUPS | EISENSTEIN COHOMOLOGY | AUTOMORPHIC-FORMS | GLOBAL COMPATIBILITY | OVERCONVERGENT MODULAR-FORMS | CONJECTURE

MATHEMATICS | FIELDS | UNITARY GROUPS | SPACES | FAMILIES | ARITHMETIC GROUPS | EISENSTEIN COHOMOLOGY | AUTOMORPHIC-FORMS | GLOBAL COMPATIBILITY | OVERCONVERGENT MODULAR-FORMS | CONJECTURE

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 04/2018, Volume 2018, Issue 8, pp. 2508 - 2534

Abstract We prove that the local components of an automorphic representation of an adelic semisimple group have equal rank in the sense of [31...

MATHEMATICS | VARIETIES | UNITARY REPRESENTATIONS | ORBIT METHOD | NOTION

MATHEMATICS | VARIETIES | UNITARY REPRESENTATIONS | ORBIT METHOD | NOTION

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 06/2018, Volume 14, Issue 5, pp. 1329 - 1345

... (aka tensor induction) representation that is critical in the sense of Deligne. For this, we relate the oddness of the associated polarized Galois representations...

Galois representations | Bloch-Kato conjecture | Fontaine-Mazur conjecture | FORMS | MATHEMATICS | AUTOMORPHY | COHOMOLOGY | UNITARY GROUPS | ADJOINT MOTIVES

Galois representations | Bloch-Kato conjecture | Fontaine-Mazur conjecture | FORMS | MATHEMATICS | AUTOMORPHY | COHOMOLOGY | UNITARY GROUPS | ADJOINT MOTIVES

Journal Article

Canadian journal of mathematics, ISSN 0008-414X, 06/2019, Volume 71, Issue 3, pp. 717 - 747

...) homogeneous left dual Banach algebra (HLDBA) over a (completely contractive) Banach algebra $A$ . We prove a Gelfand-type representation theorem showing that every HLDBA over A has a concrete realization...

Article | MATHEMATICS | group algebra | Arens product | UNITARY REPRESENTATIONS | Banach algebra | operator space | Fourier algebra | BANACH-ALGEBRAS | Theory | Mathematics | Algebra

Article | MATHEMATICS | group algebra | Arens product | UNITARY REPRESENTATIONS | Banach algebra | operator space | Fourier algebra | BANACH-ALGEBRAS | Theory | Mathematics | Algebra

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2015, Volume 334, Issue 3, pp. 1219 - 1244

.... We identify them with the quantum R matrices associated with the q-oscillator representations of $${U_q(A^{(2)}_{2n})}$$ U q ( A 2 n ( 2 ) ) , $${U_q(C^{(1)}_n)}$$ U q ( C...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SPIN REPRESENTATIONS | PHYSICS, MATHEMATICAL | UNITARY REPRESENTATIONS

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SPIN REPRESENTATIONS | PHYSICS, MATHEMATICAL | UNITARY REPRESENTATIONS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 2/2019, Volume 112, Issue 2, pp. 169 - 179

Let G be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of G...

Admissible representation | Smooth representation | p -adic reductive group | Mathematics, general | Unitary representation | Mathematics | 22D10 | Locally compact group | 22D12 | p-adic reductive group | MATHEMATICS | Algebra

Admissible representation | Smooth representation | p -adic reductive group | Mathematics, general | Unitary representation | Mathematics | 22D10 | Locally compact group | 22D12 | p-adic reductive group | MATHEMATICS | Algebra

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 2014, Volume 2014, Issue 7

Evidence is presented in some examples that an adinkra quantum number, chi o (arXiv: 0902.3830 ihep-th1), seems to play a role with regard to off-shell 4D, N =...

Superspaces | Extended Supersymmetry | MESONS | UNITARY-SPIN INDEPENDENCE | PARTICLES | AUXILIARY FIELDS MATTER | EXTENSION | MODELS | FERMI | QCD EFFECTIVE ACTION | BARYONS | N-EXTENDED SUPERSYMMETRY | PHYSICS, PARTICLES & FIELDS

Superspaces | Extended Supersymmetry | MESONS | UNITARY-SPIN INDEPENDENCE | PARTICLES | AUXILIARY FIELDS MATTER | EXTENSION | MODELS | FERMI | QCD EFFECTIVE ACTION | BARYONS | N-EXTENDED SUPERSYMMETRY | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 08/2013, Volume 54, Issue 8, p. 83508

.... A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative...

PHYSICS, MATHEMATICAL | DEFORMATION | Fourier transforms | Algebra | Lie groups | Quantization | Plane waves | Mathematical models | Representations | Quantum gravity | PHASE SPACE | MAPS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | WAVE PROPAGATION | QUANTUM GRAVITY | POISSON EQUATION | QUANTIZATION | SU-2 GROUPS | FOURIER TRANSFORMATION | UNITARY SYMMETRY

PHYSICS, MATHEMATICAL | DEFORMATION | Fourier transforms | Algebra | Lie groups | Quantization | Plane waves | Mathematical models | Representations | Quantum gravity | PHASE SPACE | MAPS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | WAVE PROPAGATION | QUANTUM GRAVITY | POISSON EQUATION | QUANTIZATION | SU-2 GROUPS | FOURIER TRANSFORMATION | UNITARY SYMMETRY

Journal Article

Monatshefte für Mathematik, ISSN 1436-5081, 2018, Volume 187, Issue 1, pp. 79 - 94

...:711–769, 2016, Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations $$\Pi '=\Pi _1\boxplus \cdots \boxplus \Pi _k$$ Π′=Π1⊞⋯⊞Π...

11R39 | Critical value | Cuspidal automorphic | Isobaric sum | 11G18 | 22E55 (Secondary) | 11F67 (Primary)11F70 | Mathematics, general | Period | Mathematics | L -function | L-function | ALGEBRA | CLASSIFICATION | ARITHMETIC PROPERTIES | FORMS | MATHEMATICS | UNITARY REPRESENTATIONS | COHOMOLOGY | GL(N) | VALUES

11R39 | Critical value | Cuspidal automorphic | Isobaric sum | 11G18 | 22E55 (Secondary) | 11F67 (Primary)11F70 | Mathematics, general | Period | Mathematics | L -function | L-function | ALGEBRA | CLASSIFICATION | ARITHMETIC PROPERTIES | FORMS | MATHEMATICS | UNITARY REPRESENTATIONS | COHOMOLOGY | GL(N) | VALUES

Journal Article

Bulletin de la Societe Mathematique de France, ISSN 0037-9484, 2014, Volume 142, Issue 2, pp. 255 - 267

...) on Speh representations of a group GL(n)(D) where D is a local non Archimedean division algebra of any characteristic.

Representations of p-adic groups | Unitary representations | Langlands program | MATHEMATICS | unitary representations | GL(N) | JACQUET-LANGLANDS CORRESPONDENCE | CLASSIFICATION | IRREDUCIBLE REPRESENTATIONS

Representations of p-adic groups | Unitary representations | Langlands program | MATHEMATICS | unitary representations | GL(N) | JACQUET-LANGLANDS CORRESPONDENCE | CLASSIFICATION | IRREDUCIBLE REPRESENTATIONS

Journal Article

Advances in applied Clifford algebras, ISSN 0188-7009, 2012, Volume 23, Issue 2, pp. 417 - 440

In the search for hypercomplex analytic functions on the halfplane, we review the construction of induced representations of the group $${G = {\rm SL}_2(\mathbb{R...

unitary representations | dual numbers | Theoretical, Mathematical and Computational Physics | Möbius transformations | Induced representation | double numbers | split-complex numbers | creation/annihilation operators | hyperbolic numbers | complex numbers | Physics | Mathematical Methods in Physics | semisimple Lie group | Applications of Mathematics | Physics, general | {\rm SL}_2(\mathbb{R}) | raising/lowering operators | parabolic numbers | ℝ | MATHEMATICS, APPLIED | Mobius transformations | PHYSICS, MATHEMATICAL | SL2(R) | OPERATORS

unitary representations | dual numbers | Theoretical, Mathematical and Computational Physics | Möbius transformations | Induced representation | double numbers | split-complex numbers | creation/annihilation operators | hyperbolic numbers | complex numbers | Physics | Mathematical Methods in Physics | semisimple Lie group | Applications of Mathematics | Physics, general | {\rm SL}_2(\mathbb{R}) | raising/lowering operators | parabolic numbers | ℝ | MATHEMATICS, APPLIED | Mobius transformations | PHYSICS, MATHEMATICAL | SL2(R) | OPERATORS

Journal Article

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