Nilpotency in type A cyclotomic quotients

TL;DR

This paper proves a conjecture regarding the nilpotency degree of cyclotomic quotients in rings that categorify part of quantum sl(k), advancing understanding in algebraic categorification.

Contribution

It establishes the nilpotency degree of cyclotomic quotients, confirming a conjecture by Brundan and Kleshchev in the context of quantum algebra.

Findings

Confirmed the conjecture on nilpotency degree

Provided explicit calculations for cyclotomic quotients

Enhanced understanding of categorification of quantum sl(k)

Abstract

We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl(k).