2021/07/06 by Nicolas Jacon, Jacon, Nicolas
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Algorithm #Chemistry #Combinatorics (math.CO) #Computation #Crystal structure #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Involution (esoterism) #Isomorphism (crystallography) #Mathematics #Pure mathematics #Representation Theory (math.RT) #math.CO #math.RT
paper · pdf · open access · doi:10.48550/arxiv.2107.02641
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/07/06 · openalex publication_date 2021/07/06 · arxiv updated 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.