Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type \(A\)

DOI10.1007/s10468-015-9530-2zbMath1332.05149arXiv1312.0021OpenAlexW2083006158MaRDI QIDQ495881

Thomas Gerber

Publication date: 15 September 2015

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0021

zbMATH Keywords

quantum groupsRobinson-Schensted correspondenceCherednik algebraalgebraic combinatoricscrystal graphAriki-Koike algebra

Mathematics Subject Classification ID

Combinatorics on words (68R15) Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08)

Related Items

Heisenberg algebra, wedges and crystals ⋮ Duality and bicrystals on infinite binary matrices ⋮ Branching graphs for finite unitary groups in nondefining characteristic ⋮ Triple crystal action in Fock spaces ⋮ Kleshchev multipartitions and extended Young diagrams ⋮ The \(A_2\) Rogers-Ramanujan identities revisited

Cites Work

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• Highest weight \(\mathfrak{sl }_2\)-categorifications. I: Crystals
• Representations of Hecke algebras at roots of unity.
• Proof of the modular branching rule for cyclotomic Hecke algebras.
• Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Branching functions of \(A_{n-1}^{(1)}\) and Jantzen-Seitz problem for Ariki-Koike algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• Crystal graphs and \(q\)-analogues of weight multiplicities for the root system \(A_ n\)
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• On the decomposition matrices of the quantized Schur algebra
• On category \(\mathcal O\) for cyclotomic rational Cherednik algebras.
• A combinatorial decomposition of higher level Fock spaces
• Crystal graphs of irreducible \(\mathcal{U}_v (\widehat{\mathfrak{sl}}_e)\)-modules of level two and Uglov bipartitions
• Laplace operators of infinite-dimensional Lie algebras and theta functions
• Harish-Chandra Series in Finite Unitary Groups and Crystal Graphs
• Heisenberg algebras and rational double affine Hecke algebras
• Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
• Three Combinatorial Models for $$ _ $$ Crystals, with Applications to Cylindric Plane Partitions
• A cyclage poset structure for Littlewood-Richardson tableaux
• Crystal isomorphisms for irreducible highest weight \(\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})\)-modules of higher level