Crystal isomorphisms and Mullineux involution II
Nicolas Jacon (LMR), C\'edric Lecouvey (IDP)
TL;DR
This paper introduces a new combinatorial algorithm for computing the Mullineux involution in symmetric groups, based on conjectural properties of crystal isomorphisms, advancing understanding in algebraic combinatorics.
Contribution
It proposes a novel, conjectural combinatorial algorithm for the Mullineux involution, linking crystal isomorphisms to symmetric group representations.
Findings
New conjectural algorithm for Mullineux involution
Reformulation of crystal isomorphisms in combinatorial terms
Potential for future proofs and applications in algebraic combinatorics
Abstract
We present a new combinatorial and conjectural algorithm for computing the Mullineux involution for the symmetric group and its Hecke algebra. This algorithm is built on a conjectural property of crystal isomorphisms which can be rephrased in a purely combinatorial way.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Quasicrystal Structures and Properties