Multiplicity function for tensor powers of modules of the \(A_n\) algebra

DOI10.1007/s11232-012-0063-0zbMath1281.17009OpenAlexW1999126946MaRDI QIDQ2636624

Olga V. Postnova, Vladimir D. Lyakhovskiĭ, Petr P. Kulish

Publication date: 30 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0063-0

zbMATH Keywords

Lie algebra representationbranching ruletensor power of modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Simple, semisimple, reductive (super)algebras (17B20) Applications of difference equations (39A60)

Related Items (14)

Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1 ^* ⋮ Generalized Pascal's triangles and singular elements of modules of Lie algebras ⋮ Generating functions of Chebyshev polynomials in three variables ⋮ Statistics of irreducible components in large tensor powers of the spinor representation for \(\mathfrak{so}_{2n+1}\) as \(n \rightarrow \infty \) ⋮ The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator ⋮ Properties of maximums of the multiplicity function ⋮ Composing arbitrarily many \(SU(N)\) fundamentals ⋮ Skew Howe duality and limit shapes of Young diagrams ⋮ The generating function of bivariate Chebyshev polynomials associated with the Lie algebra \(G_2\) ⋮ Chebyshev-Koornwinder oscillator ⋮ Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish ⋮ The limit shape of a probability measure on a tensor product of modules of the \(B_n\) algebra ⋮ Quantum group symmetries and completeness for $\boldsymbol {A}_{\boldsymbol {2n}}^{\boldsymbol{(2)}}$ open spin chains ⋮ On calculation of generating functions of Chebyshev polynomials in several variables

Cites Work

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• Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras
• Formulas for multiplicities of occurrence of irreducible components in the tensor product of representations of simple Lie algebras
• Polynomial relations among characters coming from quantum affine algebras
• On certain properties of branching coefficients for affine Lie algebras
• Symmetries of spin systems and Birman–Wenzl–Murakami algebra
• Lie groups beyond an introduction

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