Crystal graphs of irreducible \(\mathcal{U}_v (\widehat{\mathfrak{sl}}_e)\)-modules of level two and Uglov bipartitions

DOI10.1007/s10801-007-0078-zzbMath1140.17011arXivmath/0607251OpenAlexW1964028655MaRDI QIDQ2481677

Nicolas Jacon

Publication date: 14 April 2008

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607251

zbMATH Keywords

Hecke algebrasmodular representationscanonical basiscrystal graph

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08)

Related Items (10)

Cellular structures on Hecke algebras of type \(B\). ⋮ Cell structures on the blob algebra ⋮ Generalised canonical basic sets for Ariki-Koike algebras ⋮ Constructible representations and basic sets in type \(B\). ⋮ Keys and Demazure crystals for Kac-Moody algebras ⋮ Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type \(A\) ⋮ Kleshchev multipartitions and extended Young diagrams ⋮ Crystal isomorphisms for irreducible highest weight \(\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})\)-modules of higher level ⋮ On the Mullineux involution for Ariki-Koike algebras. ⋮ Uglov bipartitions and extended Young diagrams

Cites Work

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• On the parametrization of the simple modules for Ariki-Koike algebras at roots of unity.
• Canonical basic sets in type \(B_n\).
• Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
• Representations of Hecke algebras of type \(B_n\)
• Branching functions of \(A_{n-1}^{(1)}\) and Jantzen-Seitz problem for Ariki-Koike algebras
• On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
• Constructible characters and canonical bases
• The number of simple modules of the Hecke algebras of type \(G(r,1,n)\)
• Crystal graphs of higher level \(q\)-deformed Fock spaces, Lusztig \(a\)-values and Ariki-Koike algebras
• On the tensor product of two basic representations of \(U_v(\hat s l_e)\)
• Modular principal series representations
• On the classification of simple modules for cyclotomic Hecke algebras of type \(G(m,1,n)\) and Kleshchev multipartitions

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