From Macdonald polynomials to a charge statistic beyond type \(A\)

DOI10.1016/j.jcta.2011.11.013zbMath1234.05233arXiv1106.3296OpenAlexW2074483321MaRDI QIDQ662036

Cristian Lenart

Publication date: 11 February 2012

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.3296

zbMATH Keywords

Macdonald polynomialsalcove walkscharge statisticKashiwara-Nakashima columns

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Linear algebraic groups over finite fields (20G40)

Related Items

Relating the right key to the type A filling map and minimal defining chains ⋮ Macdonald polynomials and level two Demazure modules for affine \(\mathfrak{sl}_{n+1}\) ⋮ Generalized Weyl modules, alcove paths and Macdonald polynomials ⋮ Descent sets for symplectic groups ⋮ Crystal energy functions via the charge in types \(A\) and \(C\) ⋮ On combinatorial models for affine crystals ⋮ Quantum \(K\)-theory Chevalley formulas in the parabolic case ⋮ Identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules over quantum affine algebras of type \(C\) ⋮ Specializations of nonsymmetric Macdonald-Koornwinder polynomials ⋮ BGG reciprocity for current algebras ⋮ INTERVAL STRUCTURE OF THE PIERI FORMULA FOR GROTHENDIECK POLYNOMIALS ⋮ Alcove path model for \(B(\infty)\) ⋮ A uniform realization of the combinatorial \(R\)-matrix for column shape Kirillov-Reshetikhin crystals ⋮ Symplectic keys and Demazure atoms in type \(C\) ⋮ Tableau models for semi-infinite Bruhat order and level-zero representations of quantum affine algebras ⋮ A generalization of the alcove model and its applications

Cites Work

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• Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
• Affine crystals, one-dimensional sums and parabolic Lusztig \(q\)-analogues
• A combinatorial formula for Macdonald polynomials
• Haglund-Haiman-Loehr type formulas for Hall-Littlewood polynomials of type B and C
• Hall-Littlewood polynomials, alcove walks, and fillings of Young diagrams
• Lusztig's \(q\)-analogue of weight multiplicity and one-dimensional sums for affine root systems
• On combinatorial formulas for MacDonald polynomials
• Kostka polynomials and energy functions in solvable lattice models
• Symplectic standard tableaux
• Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• A bijection between type \(D_n^{(1)}\) crystals and rigged configurations
• LS galleries, the path model, and MV cycles
• Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system \(C_n\)
• Nonsymmetric Macdonald polynomials and Demazure characters.
• Crystal energy functions via the charge in types \(A\) and \(C\)
• A generalization of the alcove model and its applications
• Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems \(B_{n}\), \(C_{n}\) and \(D_{n}\)
• A combinatorial model for crystals of Kac-Moody algebras
• A symplectic jeu de taquin bijection between the tableaux of King and of De Concini
• On the quantum product of Schubert classes
• A combinatorial formula for Macdonald polynomials
• Affine Weyl Groups in K-Theory and Representation Theory