Evseev, A. and Paget, R. and Wildon, M. (2012) Character deflations and a generalization of the Murnaghan--Nakayama rule. Arxiv . (Submitted)
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| Official URL http://arxiv.org/abs/1202.0067 |
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Abstract
Given natural numbers m and n, we define a deflation map from the characters of the symmetric group S_{mn} to the characters of S_n. This map is defined by first restricting a character of S_{mn} to the wreath product S_m \wr S_n, and then taking the sum of the irreducible constituents of the restricted character on which the base group S_m \times ... \times S_m acts trivially. We prove a combinatorial rule which gives the values of the images of the irreducible characters of S_{mn} under this map. This rule is shown to generalize the Murnaghan--Nakayama rule. We also prove a number of analogous results for more general deflation maps in which the base group in the wreath product is not required to act trivially.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |
| Depositing User: | Rowena E Paget |
| Date Deposited: | 25 Apr 2012 09:42 |
| Last Modified: | 25 Apr 2012 11:08 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/29323 (The current URI for this page, for reference purposes) |
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