Combinatorics of canonical bases revisited: String data in type $A$
Representation Theory
2019-01-15 v1 Combinatorics
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 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.
Keywords
Cite
@article{arxiv.1901.04464,
title = {Combinatorics of canonical bases revisited: String data in type $A$},
author = {Volker Genz and Gleb Koshevoy and Bea Schumann},
journal= {arXiv preprint arXiv:1901.04464},
year = {2019}
}