Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of \(U_q(\mathfrak{sl}_2)\)

DOI10.1007/s00023-021-01064-xOpenAlexW3048455889MaRDI QIDQ2231917

Luc Vinet, Meri Zaimi, Nicolas Crampé

Publication date: 30 September 2021

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.04905

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantum groups (quantized function algebras) and their representations (20G42) Ring-theoretic aspects of quantum groups (16T20)

Related Items (4)

Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series ⋮ Chern-Simons theory, link invariants and the Askey-Wilson algebra ⋮ Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\) ⋮ Braid group and 𝑞-Racah polynomials

Cites Work

• The universal Askey-Wilson algebra
• Idempotents for Birman-Murakami-Wenzl algebras and reflection equation
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• ``Hidden symmetry of Askey-Wilson polynomials
• On an algebraic approach to higher dimensional statistical mechanics
• On the structure of the blob algebra
• Bannai-Ito algebras and the universal \(R\)-matrix of \(\mathfrak{osp}(1\!\!\mid\!\!2)\)
• An embedding of the universal Askey-Wilson algebra into \(\operatorname{U}_q(\mathfrak{sl}_2) \otimes U_q(\mathfrak{sl}_2) \otimes U_q(\mathfrak{sl}_2)\)
• A Temperley–Lieb Analogue for the BMW Algebra
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• One-boundary Temperley–Lieb algebras in the XXZ and loop models
• Temperley–Lieb, Brauer and Racah algebras and other centralizers of 𝔰𝔲(2)
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Revisiting the Askey–Wilson algebra with the universal R-matrix of $\boldsymbol{ \newcommand{\su}{\mathfrak{sl}} U_q(\su_2)}$
• Centralizers of the superalgebra $\mathfrak{osp}(1|2)$ : the Brauer algebra as a quotient of the Bannai–Ito algebra

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