Generalised row and column removal phenomena and $p$-Kostka numbers

TL;DR

This paper generalizes row-removal phenomena in Schur algebras, providing new reduction formulas for p-Kostka numbers and extension groups between modules, advancing understanding of algebraic structures.

Contribution

It introduces generalized row-removal principles and new reduction formulas for p-Kostka numbers and module extension groups in Schur algebras.

Findings

Established isomorphisms between subquotients of Schur algebras.

Derived new reduction formulas for p-Kostka numbers.

Extended row-removal phenomena to broader algebraic contexts.

Abstract

We explain and generalise row-removal phenomena for Schur algebras via isomorphisms between subquotients of these algebras. In particular, we prove a new reduction formulae for $p$-Kostka numbers and extension groups between Weyl and simple modules.