Derived equivalences and sl_2-categorifications for U_q(gl_n)

TL;DR

This paper constructs sl_2-categorifications for representations of quantum groups U_q(gl_n) at generic q and roots of unity, advancing the understanding of their categorical structures.

Contribution

It introduces a new construction of sl_2-categorifications for U_q(gl_n) representations applicable to both generic q and roots of unity.

Findings

Constructed sl_2-categorifications for U_q(gl_n)

Applicable to generic q and roots of unity

Enhances understanding of quantum group representations

Abstract

We give a construction of sl_2-categorifications (in the sense of Chuang-Rouquier) for representations of U_q(gl_n), for generic q and for q a root of unity.