Full runner removal theorem for Ariki-Koike algebras

2023/10/12 by Alice Dell'Arciprete, Dell'Arciprete, Alice · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2310.08156

Abstract

We consider the representation theory of the Ariki-Koike algebra, a q-deformation of the group algebra of the complex reflection group C_r \wr S_n. We define the addition of a runner full of beads for the abacus display of a multipartition and investigate some combinatorial properties of this operation. We focus our attention on the q-decomposition numbers, i.e. the polynomials arising from the Fock space representation of the quantum group U_q(\widehat\mathfraksl_e). Using Fayers' LLT-type algorithm for Ariki-Koike algebras, we relate q-decomposition numbers for different values of e for the class of e-multiregular multipartitions, by adding a full runner of beads to each component of the abacus displays for the labelling multipartitions.

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• Empty runner removal theorem for Ariki-Koike algebras

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