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arxiv: math/0610952 · v2 · submitted 2006-10-31 · 🧮 math.QA · math.CO

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A definition of the crystal commutor using Kashiwara's involution

Joel Kamnitzer , Peter Tingley
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classification 🧮 math.QA math.CO
keywords commutorcrystalinvolutionkashiwaraactionalgebracategorycomplex
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Henriques and Kamnitzer defined and studied a commutor for the category of crystals of a finite dimentional complex reductive Lie algebra. We show that the action of this commutor on highest weight elements can be expressed very simply using Kashiwara's involution on the Verma crystal.

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  1. On the action of Bender-Knuth generators of cactus group on the set of short semi-standard Young tableaux

    math.CO 2026-05 unverdicted novelty 5.0

    Explicit computation of the cactus group action via Bender-Knuth generators on the subset of short semi-standard Young tableaux, with comparison to the full set.