Monomial realization of crystal graphs for \(U_q(A_n^{(1)})\)

DOI10.1007/s00208-004-0613-3zbMath1155.17304OpenAlexW1981163249MaRDI QIDQ1777247

Jeong-Ah Kim

Publication date: 12 May 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-004-0613-3

zbMATH Keywords

quantum groupscrystal basisNakajima monomialsmonomial realizationcrystal graphspath realizationYoung wall realization

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (19)

Strip bundle realization of the crystals over Uq(D4(3)) ⋮ 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 ⋮ Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials ⋮ 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 \(U_{q}(C_{n}^{(1)})\) ⋮ 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 \(U_q(A_n^{(1)})\) ⋮ Nakajima Monomials and Crystals for Special Linear Lie Algebras ⋮ Crystal Bases and Monomials forU_q(G₂)-Modules ⋮ Strip bundle realization of the crystals over Uq(G2(1)) ⋮ The crystal ℬ(∞) and extended Nakajima monomials ⋮ Zigzag Strip Bundles and the CrystalB(∞) for Quantum Affine Algebras

Cites Work

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• Quiver varieties and tensor products
• Crystal bases for quantum classical algebras and Nakajima's monomials
• Monomial realization of crystal bases for special linear Lie algebras
• Crystalizing the q-analogue of universal enveloping algebras
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
• AFFINE CRYSTALS AND VERTEX MODELS
• CRYSTAL BASES FOR QUANTUM AFFINE ALGEBRAS AND COMBINATORICS OF YOUNG WALLS
• Quiver varieties and finite dimensional representations of quantum affine algebras

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