Core blocks for Hecke algebras of type B and sign sequences

TL;DR

This paper studies core blocks in Hecke algebras of type B, establishing their structure and parameters, and linking these to Specht modules, simple modules, and decomposition matrices across various characteristics.

Contribution

It introduces a novel parametrization of core blocks in type B Hecke algebras using two non-negative integers, connecting them to key module and block invariants.

Findings

Parameters determine Specht and simple modules in each block

The weight and multicharge of blocks are explicitly characterized

Block decomposition matrices are described in terms of these parameters

Abstract

We consider the core blocks corresponding to the Hecke algebras of type B over a field of arbitrary characteristic. To each core block B, we associate two non-negative integers which determine the indexing of the Specht modules and simple modules in the block, the weight of the block, the multicharge of the algebra (up to a shift) and the block decomposition matrix.