Lusztig data of Kashiwara-Nakashima tableaux in types $B$ and $C$
Representation Theory
2017-12-29 v2 Quantum Algebra
Abstract
We provide an explicit combinatorial description of the embedding of the crystal of Kashiwara-Nakashima tableaux in types and into that of -Lusztig data associated to a family of reduced expressions of the longest element . The description of the embedding is simple and elementary using only the Sch\"{u}tzenberger's jeu de taquin and RSK algorithm. A spinor model for classical crystals plays an important role as an intermediate object connecting Kashiwara-Nakashima tableaux and Lusztig data.
Keywords
Cite
@article{arxiv.1610.02640,
title = {Lusztig data of Kashiwara-Nakashima tableaux in types $B$ and $C$},
author = {Jae-Hoon Kwon},
journal= {arXiv preprint arXiv:1610.02640},
year = {2017}
}
Comments
41 pages, introduction is updated, the proof of Lemma 5.2 is revised with mored details, some typos in the proof of Theorem 5.7 are corrected