Enhanced nilHecke algebras and baby Verma modules

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 ${𝔰 𝔩}_{2}$ on the Grothendieck group, which is isomorphic to a baby Verma module. We upgrade the derivation into an action of the Lie algebra ${\int ↕}_{2}$ .

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Keywords

baby Verma module, $p$-dg enhanced nilHecke algebra, categorification, $\mathcal{sl}_{\mskip-2mu 2}$-action

Mathematical Subject Classification

Primary: 16W25, 18N25

Secondary: 20C08, 20G42

Milestones

Received: 25 August 2023

Revised: 12 September 2024

Accepted: 27 September 2024

Published: 7 March 2025

Authors

Elia Rizzo
Institut de Recherche en Mathématique et Physique (IRMP) Université Catholique de Louvain Louvain-la-Neuve Belgium

Pedro Vaz
Institut de Recherche en Mathématique et Physique (IRMP) Université Catholique de Louvain Louvain-la-Neuve Belgium

Vol. 7, No. 1, 2025

Elia Rizzo and Pedro Vaz

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors