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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4409| Title: | Determinants of representations of Coxeter groups |
| Authors: | Ghosh, Debarun SPALLONE, STEVEN Dept. of Mathematics |
| Keywords: | Coxeter groups Hyperoctahedral 2-Core towers Specht modules Core and quotient of partitions Determinant of representations Representation theory of symmetric group 2019 |
| Issue Date: | May-2019 |
| Publisher: | Springer Nature |
| Citation: | Journal of Algebraic Combinatorics, 49(3),229-265. |
| Abstract: | In Ayyer et al. (J Comb Theory Ser A 150:208-232, 2017), the authors characterize the partitions of n whose corresponding representations of S-n have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W. Namely, given a nontrivial multiplicative character omega of W, we give a closed formula for the number of irreducible representations of W with determinant omega. For Coxeter groups of type B-n and D-n, this is accomplished by characterizing the bipartitions associated to such representations. |
| URI: | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4409 https://doi.org/10.1007/s10801-018-0842-2 |
| ISSN: | 0925-9899 1572-9192 |
| Appears in Collections: | JOURNAL ARTICLES |
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