Small-dimensional projective representations of symmetric and alternating groups

Kleshchev, Alexander S.; Tiep, Pham Huu

doi:10.2140/ant.2012.6.1773

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Small-dimensional projective representations of symmetric and alternating groups

Alexander S. Kleshchev and Pham Huu Tiep

Vol. 6 (2012), No. 8, 1773–1816

DOI: 10.2140/ant.2012.6.1773

Abstract

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new results on branching which might be of independent interest.

Keywords

double covers of symmetric groups, modular representation theory

Mathematical Subject Classification 2010

Primary: 20C20

Secondary: 20E28, 20G40

Milestones

Received: 15 June 2011

Revised: 7 November 2011

Accepted: 15 December 2011

Published: 14 December 2012

Authors

Alexander S. Kleshchev
Department of Mathematics University of Oregon Eugene, OR 97403-1222 United States

Pham Huu Tiep
Department of Mathematics The University of Arizona 617 North Santa Rita Avenue P.O. Box 210089 Tucson, AZ 85721-0089 United States

Vol. 6, No. 8, 2012