Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra

DOI10.1080/00927870802185963zbMath1207.17030arXiv0707.2313OpenAlexW2022377702MaRDI QIDQ5301519

Tatsuro Ito, Paul M. Terwilliger

Publication date: 20 January 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.2313

zbMATH Keywords

Kac-Moody algebratridiagonal pairtetrahedron Lie algebraOnsager Lie algebra

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional Lie (super)algebras (17B65) Canonical forms, reductions, classification (15A21) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (35)

Tridiagonal pairs of \(q\)-Racah type ⋮ Krichever–Novikov Type Algebras. A General Review and the Genus Zero Case ⋮ Bidiagonal triads and the tetrahedron algebra ⋮ Compatibility and companions for Leonard pairs ⋮ Unnamed Item ⋮ Near-bipartite Leonard pairs ⋮ The classification of Leonard triples of Racah type ⋮ The Terwilliger algebras of Johnson graphs ⋮ N-point Virasoro algebras are multipoint Krichever–Novikov-type algebras ⋮ Totally bipartite Leonard pairs and totally bipartite Leonard triples of \(q\)-Racah type ⋮ A bilinear form for tridiagonal pairs of \(q\)-Serre type ⋮ Evaluation modules for the \(q\)-tetrahedron algebra ⋮ A linear map acts as a Leonard pair with each of the generators of \(U(s l_2)\) ⋮ The Leonard triples having classical type ⋮ Tridiagonal pairs of Krawtchouk type ⋮ Leonard triples from the equitable basis of \(sl_2\) ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ Bidiagonal triples ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ Tridiagonal pairs of \(q\)-Racah type and the \(\mu \)-conjecture ⋮ A classification of sharp tridiagonal pairs ⋮ Mock tridiagonal systems ⋮ HOW TO SHARPEN A TRIDIAGONAL PAIR ⋮ Double lowering operators on polynomials ⋮ Finite dimensional modules for the \(q\)-tetrahedron algebra ⋮ Representations for three-point Lie algebras of genus zero ⋮ Classical Leonard pairs having LB-TD form ⋮ A tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂ ⋮ Transition maps between the 24 bases for a Leonard pair ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ Realizations of the Witt and Virasoro Algebras and Integrable Equations ⋮ On the shape of a tridiagonal pair ⋮ Hypercube and tetrahedron algebra ⋮ A bidiagonal and tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂ ⋮ The alternating central extension of the Onsager Lie algebra

Cites Work

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• The tetrahedron algebra and its finite-dimensional irreducible modules
• The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
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• The structure of quotients of the Onsager algebra by closed ideals *
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• The $S_4$-action on tetrahedron algebra
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