Some tables of right set properties in affine Weyl groups of type A

TL;DR

This paper presents initial empirical data on the sizes of specific distinguished sets in affine Weyl groups of type A, aiming to improve computational methods for modular representation characters.

Contribution

It provides the first tables analyzing the sizes of these sets, linking combinatorial properties to computational efficiency in representation theory.

Findings

Empirical sizes of distinguished sets in affine Weyl groups of type A.

Relevance of set sizes to computational approaches for character calculations.

Initial data to guide future theoretical and computational research.

Abstract

The tables of this title are a first attempt to understand empirically the sizes of certain distinguished sets, introduced by Hankyung Ko, of elements in affine Weyl groups. The sizes are relevant to the computational efficiency of direct approaches to computing characters of modular representations of algebraic groups from characters of corresponding irreducible representations of quantum groups.