Vol. 12, No. 8, 2019

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On the classification of Specht modules with one-dimensional summands

Aubrey Piper Collins and Craig J. Dodge

Vol. 12 (2019), No. 8, 1399–1413
Abstract

This paper extends a result of James to a combinatorial condition on partitions for the corresponding Specht module to have a summand isomorphic to the unique one-dimensional FΣ-module over fields of characteristic 2. The work makes use of a recursively defined condition to reprove a result of Murphy and prove a new result for self-conjugate partitions. Finally we present a Python script which utilizes this work to test Specht modules for a one-dimensional summand.

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Keywords
representation theory, group theory, symmetric groups, Specht modules, decomposable
Mathematical Subject Classification 2010
Primary: 20C20, 20C30
Milestones
Received: 20 May 2019
Revised: 29 July 2019
Accepted: 29 August 2019
Published: 25 October 2019

Communicated by Kenneth S. Berenhaut
Authors
Aubrey Piper Collins
Department of Mathematics
Allegheny College
Meadville, PA
United States
Craig J. Dodge
Department of Mathematics
Allegheny College
Meadville, PA
United States