Representation theory of the 0-Ariki-Koike-Shoji algebras
F. Hivert, J.-C. Novelli, J.-Y. Thibon
TL;DR
This paper studies the representation theory of specialized Ariki-Koike algebras at q=0, classifying modules and connecting their Grothendieck rings to graded Hopf algebras and quasi-symmetric functions.
Contribution
It provides a detailed classification of modules and links the algebraic structures to Mantaci-Reutenauer and Poirier's quasi-symmetric functions, revealing new structural insights.
Findings
Classification of simple and projective modules
Description of restrictions, inductions, and Cartan invariants
Identification of Grothendieck rings with graded Hopf algebras
Abstract
We investigate the representation theory of certain specializations of the Ariki-Koike algebras, obtained by setting in a suitably normalized version of Shoji's presentation. We classify the simple and projective modules, and describe restrictions, induction products, Cartan invariants and decomposition matrices. This allows us to identify the Grothendieck rings of the towers of algebras in terms of certain graded Hopf algebras known as the Mantaci-Reutenauer descent algebras, and Poirier Quasi-symmetric functions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics