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

Kleshchev, Alexander; Livesey, Michael

doi:10.5802/art.22

Kleshchev, Alexander ¹ ; Livesey, Michael ²

¹ Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
² School of Mathematics, University of Manchester, Manchester, M139PL, U.K.

Annals of Representation Theory, Volume 2 (2025) no. 1, pp. 85-171.

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.

Received: 2023-10-05
Revised: 2024-12-09
Accepted: 2025-01-16
Published online: 2025-03-05

DOI: 10.5802/art.22

Classification: 20C20, 20C25, 20C30

Author's affiliations:

Kleshchev, Alexander ¹; Livesey, Michael ²

¹ Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
² School of Mathematics, University of Manchester, Manchester, M139PL, U.K.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Kleshchev, Alexander; Livesey, Michael. RoCK blocks for double covers of symmetric groups over a complete discrete valuation ring. Annals of Representation Theory, Volume 2 (2025) no. 1, pp. 85-171. doi : 10.5802/art.22. https://art.centre-mersenne.org/articles/10.5802/art.22/

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