Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Decomposition numbers of 2-parts spin representations of symmetric groups in characteristic 2

Lucia Morotti

Abstract

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper bounds are found.

Decomposition numbers of 2-parts spin representations of symmetric groups in characteristic 2

Abstract

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper bounds are found.
Paper Structure (7 sections, 18 theorems, 132 equations)

This paper contains 7 sections, 18 theorems, 132 equations.

Table of Contents

  1. Introduction
  2. Notation and basic results
  3. Projective modules
  4. Proof of Theorem \ref{['t1']}
  5. Proof of Theorem \ref{['T100822']}
  6. Proof of Theorem \ref{['T170223']}
  7. Examples

Key Result

Theorem 1.1

If $0\leq a\leq\lfloor(n-1)/2\rfloor$ and $\mu\in{\mathscr {P}}_2(n)$ is such that $D^\mu$ is a composition factor of $S((n-a,a),\varepsilon)$ then $\mu$ has at most 2 parts or it is the double of a partition with at most 2 parts.

Theorems & Definitions (30)

  • Theorem 1.1
  • Definition 1.2
  • Definition 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Theorem 1.6
  • Lemma 2.1
  • Lemma 2.2
  • proof : Proof of Theorem \ref{['c1']}
  • Lemma 2.3
  • ...and 20 more