Crystal bases for quantum classical algebras and Nakajima's monomials

DOI10.2977/prims/1145475492zbMath1072.17007OpenAlexW2051876407MaRDI QIDQ1769590

Dong-Uy Shin, Jeong-Ah Kim, Seok-Jin Kang

Publication date: 4 April 2005

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145475492

zbMATH Keywords

monomialsquantum algebrasYoung tableaucrystal bases

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Representation theory for linear algebraic groups (20G05)

Related Items (21)

Strip bundle realization of the crystals over Uq(D4(3)) ⋮ Level 0 Monomial Crystals ⋮ Extended Nakajima monomials and crystal \({\mathcal B}(\infty)\) for finite simple Lie algebras ⋮ Crystal bases as tuples of integer sequences ⋮ Modified Nakajima monomials and the crystal \(B(\infty )\) ⋮ Zigzag strip bundles and crystals ⋮ Zigzag strip bundles and highest weight crystals ⋮ Zigzag strip bundles and crystals. II ⋮ Compression of Nakajima monomials in type A and C ⋮ Generalized Young walls for classical Lie algebras ⋮ Monomial Realization of the Crystals OverU_q(A_∞) and the Quantum Monster Algebra ⋮ Zigzag strip bundle realization of \(B(\lambda_{0})\) over \(U_{q}(C_{n}^{(1)})\) ⋮ t-Analogs of q-Characters of Quantum Affine Algebras of Type E6, E7, E8 ⋮ Auslander-Reiten numbers games ⋮ Monomial realization of crystal bases \(B(\infty)\) for the quantum finite algebras ⋮ Monomial Realization of the Tensor Product of Crystals for Quantum Finite Algebras ⋮ Nakajima monomials, Young walls and Kashiwara embedding for \(U_q(A_n^{(1)})\) ⋮ Monomial realization of crystal graphs for \(U_q(A_n^{(1)})\) ⋮ Nakajima Monomials and Crystals for Special Linear Lie Algebras ⋮ Crystal Bases and Monomials forU_q(G₂)-Modules ⋮ Zigzag Strip Bundles and the CrystalB(∞) for Quantum Affine Algebras

Cites Work

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• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Quiver varieties and tensor products
• Monomial realization of crystal bases for special linear Lie algebras
• Insertion Scheme for the Classical Lie Algebras
• CRYSTAL BASES FOR QUANTUM AFFINE ALGEBRAS AND COMBINATORICS OF YOUNG WALLS
• Young wall realization of crystal bases for classical Lie algebras

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