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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/3362| Title: | Representations of symmetric groups with non-trivial determinant |
| Authors: | Ayyer, Arvind Prasad, Amritanshu SPALLONE, STEVEN Dept. of Mathematics |
| Keywords: | Representations Symmetric groups Non-trivial determinant Symmetric group Irreducible representations Permutation representations Determinants Core Quotients Core Towers Bell numbers 2017 |
| Issue Date: | Aug-2017 |
| Publisher: | Elsevier B.V. |
| Citation: | Journal of Combinatorial Theory Series A, 150, 208-232. |
| Abstract: | We give a closed formula for the number of partitions A of n such that the corresponding irreducible representation V-lambda of S-n has non-trivial determinant. We determine how many of these partitions are self-conjugate and how many are hooks. This is achieved by characterizing the 2-core towers of such partitions. We also obtain a formula for the number of partitions of n such that the associated permutation representation of S-n has non-trivial determinant. |
| URI: | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/3362 https://doi.org/10.1016/j.jcta.2017.03.004 |
| ISSN: | 0097-3165 |
| Appears in Collections: | JOURNAL ARTICLES |
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