Paths, Demazure crystals, and symmetric functions

DOI10.1063/1.1286284zbMath0971.17006arXivq-alg/9612018OpenAlexW2082260736MaRDI QIDQ2738198

Atsuo Kuniba, Kailash C. Misra, Taichiro Takagi, Jun Uchiyama, Masato Okado

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9612018

zbMATH Keywords

symmetric functionpathDemazure characterDemazure crystalquantum affine Lie algebra

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23)

Related Items (8)

Weyl, Demazure and fusion modules for the current algebra of \(\mathfrak{sl}_{r+1}\) ⋮ Littelmann paths for the basic representation of an affine Lie algebra ⋮ Crystal energy functions via the charge in types \(A\) and \(C\) ⋮ Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ Demazure crystals of type \(A_{n}\) and Young walls ⋮ Demazure modules, fusion products and \(Q\)-systems ⋮ Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties

Cites Work

• Kostka polynomials and energy functions in solvable lattice models
• Perfect crystals of quantum affine Lie algebras
• Demazure modules and perfect crystals
• Crystals for Demazure modules of classical affine Lie algebras
• The crystal base and Littelmann's refined Demazure character formula
• Characters of Demazure modules and solvable lattice models
• One-dimensional configuration sums in vertex models and affine Lie algebra characters
• Crystalizing the q-analogue of universal enveloping algebras
• On the Combinatorics of Row and Corner Transfer Matrices of the $A^{(1)}_{n-1}$ Restricted Face Models
• AFFINE CRYSTALS AND VERTEX MODELS
• STRINGS, PATHS AND STANDARD TABLEAUX
• Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties

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