A definition of the crystal commutor using Kashiwara's involution

DOI10.1007/s10801-008-0136-1zbMath1236.17010arXivmath/0610952OpenAlexW2081701595MaRDI QIDQ1016153

Joel Kamnitzer, Peter Tingley

Publication date: 4 May 2009

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

Full work available at URL: https://arxiv.org/abs/math/0610952

zbMATH Keywords

crystalscoboundary categorycrystal commutor

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (11)

Virtual crystals and Nakajima monomials ⋮ Connecting marginally large tableaux and rigged configurations via crystals ⋮ A combinatorial geometric Satake equivalence ⋮ Categorical geometric skew Howe duality ⋮ Rigged configurations and the \(\ast\)-involution ⋮ Crystal energy functions via the charge in types \(A\) and \(C\) ⋮ Categorical braid group actions and cactus groups ⋮ Keys and Demazure crystals for Kac-Moody algebras ⋮ Coboundary categories and local rules ⋮ On the combinatorics of crystal graphs, II. The crystal commutor ⋮ Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras

Cites Work

• Unnamed Item
• Crystals, quiver varieties, and coboundary categories for Kac-Moody algebras
• Cones, crystals, and patterns
• The crystal base and Littelmann's refined Demazure character formula
• The crystal structure on the set of Mirković-Vilonen polytopes
• Crystals and coboundary categories

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