Carter-Payne homomorphisms and Jantzen filtrations

TL;DR

This paper establishes a q-analogue of the Carter-Payne theorem for large partition differences, identifies a Jantzen filtration layer containing Carter-Payne homomorphisms, and explores their composition.

Contribution

It introduces a q-analogue of the Carter-Payne theorem, linking it to Jantzen filtrations and homomorphism composition, advancing understanding in modular representation theory.

Findings

Proves a q-analogue of the Carter-Payne theorem for large partition differences

Identifies a specific layer of the Jantzen filtration containing Carter-Payne homomorphisms

Shows how Carter-Payne homomorphisms compose within this framework

Abstract

We prove a q-analogue of the Carter-Payne theorem in the case where the differences between the parts of the partitions are sufficiently large. We identify a layer of the Jantzen filtration which contains the image of these Carter-Payne homomorphisms and we show how these homomorphisms compose.