Stuttering blocks of Ariki–Koike algebras

Rostam, Salim

doi:10.5802/alco.40

Rostam, Salim ¹

¹ Laboratoire de Mathématiques de Versailles UVSQ CNRS Université Paris-Saclay 78035 Versailles (France)

Algebraic Combinatorics, Volume 2 (2019) no. 1, pp. 75-118.

Abstract

We study a shift action defined on multipartitions and on residue multisets of their Young diagrams. We prove that the minimal orbit cardinality among all multipartitions associated with a given multiset depends only on the orbit cardinality of the multiset. Using abaci, this problem reduces to a convex optimisation problem over the integers with linear constraints. We solve it by proving an existence theorem for binary matrices with prescribed row, column and block sums. Finally, we give some applications to the representation theory of the Hecke algebra of the complex reflection group $G (r, p, n)$ .

Received: 2017-11-29
Revised: 2018-07-26
Accepted: 2018-08-13
Published online: 2019-02-04

MR Zbl

DOI: 10.5802/alco.40

Classification: 20C08
Keywords: Ariki–Koike algebras, multipartitions, residues, abacus, Hecke algebras

Author's affiliations:

Rostam, Salim ¹

¹ Laboratoire de Mathématiques de Versailles UVSQ CNRS Université Paris-Saclay 78035 Versailles (France)

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Rostam, Salim. Stuttering blocks of Ariki–Koike algebras. Algebraic Combinatorics, Volume 2 (2019) no. 1, pp. 75-118. doi : 10.5802/alco.40. https://alco.centre-mersenne.org/articles/10.5802/alco.40/

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