A crystal embedding into Lusztig data of type $A$
Representation Theory
2019-07-04 v2 Combinatorics
Quantum Algebra
Abstract
Let be a reduced expression of the longest element in the Weyl group of type , which is adapted to a Dynkin quiver with a single sink. We present a simple description of the crystal embedding of Young tableaux of arbitrary shape into -Lusztig data, which also gives an algorithm for the transition matrix between Lusztig data associated to reduced expressions adapted to quivers with a single sink.
Keywords
Cite
@article{arxiv.1606.06804,
title = {A crystal embedding into Lusztig data of type $A$},
author = {Jae-Hoon Kwon},
journal= {arXiv preprint arXiv:1606.06804},
year = {2019}
}
Comments
22 pages, minor corrections; introduction revised, statements and proofs of Proposition 4.1 and Theorem 4.2 revised, comments added on Remark 4.4, typos corrected