University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar > Character deflations, wreath products and Foulkes' Conjecture

## Character deflations, wreath products and Foulkes' ConjectureAdd to your list(s) Download to your calendar using vCal - Mark Wildon, Royal Holloway, University of London
- Thursday 17 January 2013, 17:00-18:00
- Watson Building, Lecture Room C.
If you have a question about this talk, please contact David Craven. Foulkes’ Conjecture is one of the main open problems in algebraic combinatorics: it states that if ab into b sets each of size a contains the permutation character of S acting on set partitions of the same set into _{ab}a sets each of size b. In my talk I will present a new approach to Foulkes’ Conjecture based on a deflation map that sends characters of the wreath product of S with _{a}S to characters of _{b}S. Our main result is a combinatorial rule for the values taken by these deflated character. This rule generalizes the Murnaghan–Nakayama rule and Young’s rule, and leads to a new algorithm for computing the irreducible constituents of Foulkes characters. Using this algorithm we have verified Foulkes’ Conjecture in several new cases, including all _{b}a, b such that a + b ≤ 18.This talk is on joint work with Anton Evseev and Rowena Paget. This talk is part of the Birmingham and Warwick Algebra Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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