RoCK blocks for double covers of symmetric groups over a complete discrete valuation ring

TL;DR

This paper proves that RoCK blocks for double covers of symmetric groups over an algebraically closed field can be lifted to a discrete valuation ring, maintaining derived equivalence with their Brauer correspondents, using purely representation-theoretic methods.

Contribution

It demonstrates the lift of RoCK blocks to a discrete valuation ring and establishes their splendid derived equivalence with Brauer correspondents, independent of quiver Hecke superalgebras.

Findings

RoCK blocks lift to discrete valuation rings.

Lifted blocks are splendidly derived equivalent to Brauer correspondents.

Techniques are purely from finite group representation theory.

Abstract

Recently the authors proved the existence of RoCK blocks for double covers of symmetric groups over an algebraically closed field of odd characteristic. In this paper we prove that these blocks lift to RoCK blocks over a suitably defined discrete valuation ring. Such a lift is even splendidly derived equivalent to its Brauer correspondent. We note that the techniques used in the current article are almost completely independent from those previously used by the authors. In particular, we do not make use of quiver Hecke superalgebras and the main result is proved using methods solely from the theory of representations of finite groups. Therefore, this paper much more resembles the work of Chuang and Kessar, where RoCK blocks for symmetric groups were constructed.