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Title: The varieties for some Specht modules
Authors: Lim, Kay Jin
Keywords: DRNTU::Science::Mathematics::Algebra
Issue Date: 2009
Source: Lim, K. J. (2009). The varieties for some Specht modules. Journal of Algebra, 321(8), 2287-2301.
Series/Report no.: Journal of algebra
Abstract: J. Carlson introduced the cohomological and rank variety for a module over a finite group algebra. We give a general form for the largest component of the variety for the Specht module for the partition (pp) of p2 restricted to a maximal elementary abelian p-subgroup of rank p. We determine the varieties of a large class of Specht modules corresponding to p-regular partitions. To any partition of np of not more than p parts with empty p-core we associate a unique partition Φ(μ) of np, where the rank variety of the restricted Specht module SμEn↓ to a maximal elementary abelian p-subgroup En of rank n is V#En (k) if and only if V#En (SΦ(μ)) = V#En (k). In some cases where Φ(μ) is a 2-part partition, we show that the rank variety V#En (Sμ) is V#En (k). In particular, the complexity of the Specht module Sμ is n.
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.01.016
Rights: © 2009 Elsevier Inc. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Algebra, Elsevier Inc. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI:].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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