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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
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Abstract |
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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 -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
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Mathematical Subject Classification 2010
Primary: 20C20, 20C30
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Milestones
Received: 20 May 2019
Revised: 29 July 2019
Accepted: 29 August 2019
Published: 25 October 2019
Communicated by Kenneth S. Berenhaut
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Authors |
| Aubrey Piper Collins | |
| Department of Mathematics Allegheny College Meadville, PA United States |
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| Craig J. Dodge | |
| Department of Mathematics Allegheny College Meadville, PA United States |
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