Abstract
We give a formula for the crystal structure on the integer points of the string polytopes and the *-crystal structure on the integer points of the string cones of type A for arbitrary reduced words. As a byproduct, we obtain defining inequalities for Nakashima–Zelevinsky string polytopes. Furthermore, we give an explicit description of the Kashiwara *-involution on string data for a special choice of reduced word.
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V. Genz is supported by SFB/TRR 191.
G. Koshevoy is supported by RSF 16-11-10075 and SFB/TRR 191.
B. Schumann is supported by SFB/TRR 191.
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GENZ, V., KOSHEVOY, G. & SCHUMANN, B. COMBINATORICS OF CANONICAL BASES REVISITED: STRING DATA IN TYPE A. Transformation Groups 27, 867–895 (2022). https://doi.org/10.1007/s00031-021-09668-7
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DOI: https://doi.org/10.1007/s00031-021-09668-7