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Mullineux involution and crystal isomorphisms

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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03278927
Contributor : Nicolas Jacon Connect in order to contact the contributor
Submitted on : Tuesday, July 6, 2021 - 9:56:56 AM
Last modification on : Thursday, October 14, 2021 - 1:10:04 PM
Long-term archiving on: : Thursday, October 7, 2021 - 6:18:00 PM

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Mullinvo13:01p4.pdf
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  • HAL Id : hal-03278927, version 1
  • ARXIV : 2107.02641

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CNRS | URCA | INSMI | LMR

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Nicolas Jacon. Mullineux involution and crystal isomorphisms. 2021. ⟨hal-03278927⟩

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