Character deflations and a generalization of the Murnaghan--Nakayama rule

Evseev, A. and Paget, R. and Wildon, M. (2012) Character deflations and a generalization of the Murnaghan--Nakayama rule. Arxiv . (Submitted) (Full text available)

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http://arxiv.org/abs/1202.0067

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 Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial ScienceFaculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Rowena E Paget 25 Apr 2012 09:42 25 Apr 2012 11:08 http://kar.kent.ac.uk/id/eprint/29323 (The current URI for this page, for reference purposes)