The varieties for some Specht modules
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 vari...
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| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/102335 http://hdl.handle.net/10220/18897 |
| _version_ | 1811695411696500736 |
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| author | Lim, Kay Jin |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Lim, Kay Jin |
| author_sort | Lim, Kay Jin |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:23:03Z |
| format | Journal Article |
| id | ntu-10356/102335 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:23:03Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1023352023-02-28T19:23:05Z The varieties for some Specht modules Lim, Kay Jin School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Algebra 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. Accepted version 2014-03-14T03:02:09Z 2019-12-06T20:53:38Z 2014-03-14T03:02:09Z 2019-12-06T20:53:38Z 2009 2009 Journal Article Lim, K. J. (2009). The varieties for some Specht modules. Journal of Algebra, 321(8), 2287-2301. 0021-8693 https://hdl.handle.net/10356/102335 http://hdl.handle.net/10220/18897 10.1016/j.jalgebra.2009.01.016 en Journal of algebra © 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]. 16 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Algebra Lim, Kay Jin The varieties for some Specht modules |
| title | The varieties for some Specht modules |
| title_full | The varieties for some Specht modules |
| title_fullStr | The varieties for some Specht modules |
| title_full_unstemmed | The varieties for some Specht modules |
| title_short | The varieties for some Specht modules |
| title_sort | varieties for some specht modules |
| topic | DRNTU::Science::Mathematics::Algebra |
| url | https://hdl.handle.net/10356/102335 http://hdl.handle.net/10220/18897 |
| work_keys_str_mv | AT limkayjin thevarietiesforsomespechtmodules AT limkayjin varietiesforsomespechtmodules |