Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape

DOI10.1112/plms/pdm034zbMath1219.17013arXivmath/0510017OpenAlexW2085096252MaRDI QIDQ5460535

Daisuke Sagaki, Satoshi Naito

Publication date: 29 April 2008

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510017

zbMATH Keywords

affine Lie algebraweight latticepath crystalLakshmibai-Seshadri pathlevel-zero integral weight

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Algebraic combinatorics (05E99)

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Virtualization map for the Littelmann path model ⋮ Kirillov–Reshetikhin crystals B^7,s for type E₇⁽¹⁾ ⋮ Demazure character formula for semi-infinite flag varieties ⋮ Lakshmibai–Seshadri paths for hyperbolic Kac–Moody algebras of rank 2 ⋮ Uniform description of the rigged configuration bijection ⋮ Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials ⋮ Semi-infinite Lakshmibai-Seshadri path model for level-zero extremal weight modules over quantum affine algebras ⋮ Existence of Kirillov-Reshetikhin crystals for multiplicity-free nodes ⋮ Weyl modules, Demazure modules and finite crystals for non-simply laced type ⋮ A uniform approach to soliton cellular automata using rigged configurations ⋮ Rigged configuration bijection and proof of the \(X = M\) conjecture for nonexceptional affine types ⋮ On higher level Kirillov-Reshetikhin crystals, Demazure crystals, and related uniform models

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