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Mullineux involution and crystal isomorphisms
- Publication Year :
- 2021
-
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.
- Subjects :
- Mathematics - Combinatorics
Mathematics - Representation Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2107.02641
- Document Type :
- Working Paper