Mullineux involution and crystal isomorphisms
Combinatorics
2021-07-07 v1 Representation Theory
Abstract
We develop a new approach for the computation of the Mullineux involution for the symmetric group and its Hecke algebra using the notion of crystal isomorphism and the Iwahori-Matsumoto involution for the affine Hecke algebra of type A. As a consequence, we obtain several new elementary combinatorial algorithms for its computation, one of which is equivalent to Xu's algorithm (and thus Mullineux' original algorithm). We thus obtain a simple interpretation of these algorithms and a new elementary proof that they indeed compute the Mullineux involution.
Keywords
Cite
@article{arxiv.2107.02641,
title = {Mullineux involution and crystal isomorphisms},
author = {Nicolas Jacon},
journal= {arXiv preprint arXiv:2107.02641},
year = {2021}
}