Work

Elementary methods for splitting representations of rook monoids: A gentle introduction to groupoids

Year: 2025

Type: article

Abstract: In this paper, we show that the algebra of the colored rook monoid [Formula: see text], i.e. the monoid of [Formula: see text] matrices with at most one non-zero entry (an [Formula: see text]th root of unity) in each column and row, is the algebra of a finite groupoid, thus is endowed with a [Formula: see text]-algebra structure. This new perspective uncovers the representation theory of these monoid algebras by making manifest their decomposition in irreducible modules.

Source: International Journal of Geometric Methods in Modern Physics

DOI: 10.1142/s0219887825400444

Authors: Joseph Ben Geloun, Gérard H. E. Duchamp, Christophe Tollu

Institutions: Centre National de la Recherche Scientifique, Université Sorbonne Paris Nord, Université d'Abomey-Calavi, Laboratoire d'Informatique de Paris-Nord

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4408910167

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