Finite-dimensional irreducible modules of the Racah algebra at characteristic zero

DOI10.3842/SIGMA.2020.018zbMath1436.81054arXiv1910.11446MaRDI QIDQ1987289

Sarah Bockting-Conrad, Hau-Wen Huang

Publication date: 14 April 2020

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.11446

zbMATH Keywords

quadratic algebrairreducible modulesRacah algebrauniversal propertytridiagonal pairs

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quadratic and Koszul algebras (16S37)

Related Items (13)

The Racah algebra: An overview and recent results ⋮ Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series ⋮ The Clebsch-Gordan rule for \(U(\mathfrak{sl}_2)\), the Krawtchouk algebras and the Hamming graphs ⋮ Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\) ⋮ Matrix elements of SO(3) in sl3 representations as bispectral multivariate functions ⋮ Bethe ansatz diagonalization of the Heun-Racah operator ⋮ Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero ⋮ Representations of the rank two Racah algebra and orthogonal multivariate polynomials ⋮ The Clebsch-Gordan coefficients of \(U(\mathfrak{sl}_2)\) and the Terwilliger algebras of Johnson graphs ⋮ Finite-dimensional irreducible modules of the universal Askey-Wilson algebra at roots of unity ⋮ The Casimir elements of the Racah algebra ⋮ Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type \((C_1^\vee,C_1)\) ⋮ Finite-dimensional modules of the universal Askey-Wilson algebra and DAHA of type \((C_1^\vee ,C_1)\)

Cites Work

• Superintegrability in two dimensions and the Racah-Wilson algebra
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
• A discrete realization of the higher rank Racah algebra
• Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type \((C_1^\vee,C_1)\)
• Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero
• The Racah algebra as a subalgebra of the Bannai-Ito algebra
• Embeddings of the Racah algebra into the Bannai-Itô algebra
• The Classification of Finite-Dimensional Irreducible Modules of Bannai/Ito Algebra
• A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator
• The universal enveloping algebra of sl2 and the Racah algebra
• The classification of finite-dimensional irreducible modules of the Racah algebra
• Symmetrical Coupling of Three Angular Momenta
• The equitable Racah algebra from three $\mathfrak {su}(1,1)$ algebras
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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