Large dimensional homomorphism spaces between Weyl modules and Specht modules

TL;DR

This paper demonstrates the existence of large homomorphism spaces between Weyl modules, revealing new structural insights and providing explicit examples of arbitrarily large homomorphism spaces for fixed parameters.

Contribution

It introduces a family of Weyl module pairs with at least 2-dimensional homomorphism spaces and shows these can be arbitrarily large for fixed parameters.

Findings

Existence of pairs of Weyl modules with at least 2-dimensional homomorphism spaces

Construction of arbitrarily large homomorphism spaces for fixed parameters

New structural understanding of homomorphism spaces in representation theory

Abstract

We give a family of pairs of Weyl modules for which the corresponding homomorphism space is at least 2-dimensional. Using this result we show that for fixed parameters $e>0$ and $p\geq 0$ there exist arbitrarily large homomorphism spaces between pairs of Weyl modules.