A tensor product theorem related to perfect crystals.

DOI10.1016/S0021-8693(03)00349-1zbMath1039.17017arXivmath/0111288MaRDI QIDQ1403899

Masato Okado, Anne Schilling, Mark Shimozono

Publication date: 20 August 2003

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

Full work available at URL: https://arxiv.org/abs/math/0111288

zbMATH Keywords

perfect crystalquantum affine algebrahighest weight modulecrystal graphtensor product theorem

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23)

Related Items (11)

Virtual crystals and Nakajima monomials ⋮ Similarity and Kirillov-Schilling-Shimozono bijection ⋮ Affine geometric crystal of \(A_n^{(1)}\) and limit of Kirillov-Reshetikhin perfect crystals ⋮ Realization of affine type \(A\) Kirillov-Reshetikhin crystals via polytopes ⋮ Limits of multiplicities in excellent filtrations and tensor product decompositions for affine Kac-Moody algebras ⋮ Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials ⋮ Realization of Kirillov-Reshetikhin crystals \(B^{1,s}\) for \(\widehat{\mathfrak{sl}}_n\) using Nakajima monomials ⋮ A note on tensor categories of Lie type \(E_{9}\) ⋮ Affine type \(A\) geometric crystal on the Grassmannian ⋮ $A^{(1)}_{n}$ -Geometric Crystal Corresponding to Dynkin Index i=2 and Its Ultra-Discretization ⋮ ON TENSOR PRODUCT DECOMPOSITION OF $\widehat{\mathfrak{sl}}(n)$ MODULES

Cites Work

• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Perfect crystals of quantum affine Lie algebras
• Finite-dimensional representations of quantum affine algebras
• Quantized affine algebras and crystals with core
• Crystal bases of modified quantized enveloping algebra
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Fermionic formulas for level-restricted generalized Kostka polynomials and coset branching functions
• Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
• A bijection between Littlewood-Richardson tableaux and rigged configurations
• AFFINE CRYSTALS AND VERTEX MODELS
• Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾
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