Core blocks of Ariki-Koike algebras II: the weight of a core block
Matthew Fayers
TL;DR
This paper investigates the combinatorial structure of blocks in Ariki-Koike algebras, focusing on weights, hubs, and the affine Weyl group action, providing new insights into their interrelations.
Contribution
It characterizes which pairs of weight and hub occur as block parameters and analyzes the affine Weyl group's action on these blocks.
Findings
Characterization of possible (w, theta) pairs in blocks
Analysis of affine Weyl group action on blocks
Enhanced understanding of combinatorial block structure
Abstract
We study combinatorial blocks of multipartitions, exploring further the notions of weight, hub and core block introduced by the author in earlier papers. We answer the question of which pairs (w,theta) occur as the weight and hub of a block, and we examine the action of the affine Weyl group on the set of blocks.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics