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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.||URI:||https://hdl.handle.net/10356/102335
|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: http://dx.doi.org/10.1016/j.jalgebra.2009.01.016].||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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