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Core blocks for Hecke algebras of type B and sign sequences

Sinead Lyle

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.

Core blocks for Hecke algebras of type B and sign sequences

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.
Paper Structure (10 sections, 24 theorems, 54 equations)

This paper contains 10 sections, 24 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Multipartitions and abacus configurations
  4. The Ariki-Koike algebra
  5. Core blocks when $r=2$
  6. Sign sequences
  7. Indexing the block decomposition matrices corresponding to core blocks
  8. The Fock space representation
  9. Decomposition matrices
  10. Summary and examples

Key Result

Lemma 2.1

Let $\boldsymbol \lambda \in \Lambda^r$ and $\mathfrak{a} \in \mathbb{Z}^r$. All residues below are with repect to $\mathfrak{a}$ as are all abacus configurations.

Theorems & Definitions (43)

  • Lemma 2.1
  • Example
  • Lemma 2.2: Fayers:Cores
  • Proposition 2.3: LM:Blocks
  • Example
  • Example
  • Example
  • Lemma 3.1: Fayers:Cores
  • Corollary 3.2
  • Lemma 3.3
  • ...and 33 more