The degenerate analogue of Ariki's categorification theorem

TL;DR

This paper derives the degenerate analogue of Ariki's categorification theorem over the complex numbers using Schur-Weyl duality and Kazhdan-Lusztig theory, and discusses related topics like Young modules and Ringel duality.

Contribution

It provides a new derivation of the degenerate Ariki's categorification theorem leveraging Schur-Weyl duality and Kazhdan-Lusztig conjecture, expanding understanding of categorification in type A.

Findings

Derived the degenerate Ariki's categorification theorem over C.

Connected Schur-Weyl duality with Kazhdan-Lusztig theory.

Explored related topics like Young modules and Ringel duality.

Abstract

We explain how to deduce the degenerate analogue of Ariki's categorification theorem over the ground field C as an application of Schur-Weyl duality for higher levels and the Kazhdan-Lusztig conjecture in finite type A. We also discuss some supplementary topics, including Young modules, tensoring with sign, tilting modules and Ringel duality.