Enhanced nilHecke algebras and baby Verma modules

TL;DR

This paper introduces a derivation on enhanced nilHecke algebras over fields of characteristic p, leading to new algebraic structures and actions related to quantum sl2 and baby Verma modules.

Contribution

It defines a derivation on enhanced nilHecke algebras that produces a p-dg algebra and constructs functors inducing an sl(2) action on the Grothendieck group, connecting to baby Verma modules.

Findings

Derived a p-dg algebra from enhanced nilHecke algebra

Constructed functors realizing quantum sl2 action

Established isomorphism with baby Verma modules

Abstract

We define a derivation on the enhanced nilHecke algebra yielding a p-dg algebra when working over a field of characteristic p. We define functors on the category of p-dg modules resulting in an action of small quantum sl2 on the Grothendieck group, which is isomorphic to a baby Verma module. We upgrade the derivation into an action of the Lie algebra sl(2).