Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems \(B_{n}\), \(C_{n}\) and \(D_{n}\)

DOI10.1016/j.ejc.2005.01.006zbMath1107.05096arXivmath/0406574OpenAlexW2022032060MaRDI QIDQ2368711

Cédric Lecouvey

Publication date: 28 April 2006

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

Full work available at URL: https://arxiv.org/abs/math/0406574

zbMATH Keywords

statistic on tableaux

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05)

Related Items

Duality and bicrystals on infinite binary matrices, Crystal energy functions via the charge in types \(A\) and \(C\), Stabilization of the Brylinski-Kostant filtration and limit of Lusztig \(q\)-analogues, From Macdonald polynomials to a charge statistic beyond type \(A\), A positive combinatorial formula for symplectic Kostka-Foulkes polynomials. I: Rows, Atomic decomposition of characters and crystals, Combinatorics of generalized exponents, Lusztig's \(t\)-analogue of weight multiplicity via crystals

Cites Work

• A plactic algebra for semisimple Lie algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Schensted-type correspondence, plactic monoid, and jeu de taquin for type \(C_n\)
• Schensted-type correspondences and plactic monoids for types \(B_n\) and \(D_n\)
• A combinatorial proof of a recursion for the \(q\)-Kostka polynomials
• Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system \(C_n\)
• Crystal graphs and \(q\)-analogues of weight multiplicities for the root system \(A_ n\)
• The characters of the group GL(n, q)
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