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Specht modules
for partitions $(k,3,3)$ have no one-dimensional summand
Craig J. Dodge and Elijah Van Vlack |
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Vol. 16 (2023), No. 4, 659–672
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Abstract |
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We consider the Specht module graphs for partitions of the form and determine the parity of the number of paths on these directed graphs. For values of the partition is Lucas perfect, so the associated Specht module will have a one-dimensional summand exactly when the number of paths on the graph is odd. By establishing equivalence classes on the set of paths and comparing to smaller partitions, we are able to demonstrate that none of these Specht modules have a one-dimensional summand. |
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Keywords
Specht modules, standard tableau, symmetric group
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Mathematical Subject Classification
Primary: 20C20, 20C30
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Milestones
Received: 10 June 2022
Revised: 27 September 2022
Accepted: 27 September 2022
Published: 31 October 2023
Communicated by Ken Ono
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Authors |
| Craig J. Dodge | |
| Department of Mathematics Allegheny College Meadville, PA United States |
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| Elijah Van Vlack | |
| Department of Mathematics Allegheny College Meadville, PA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
