Character deflations, wreath products and Foulkes' Conjecture

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• 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 a ≤ b then the permutation character of the symmetric group S_ab acting on set partitions of a set of size ab into b sets each of size a contains the permutation character of S_ab acting on set partitions of the same set into 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_a with S_b to characters of S_b. 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 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:

• Birmingham and Warwick Algebra Seminar
• School of Mathematics Events
• Watson Building, Lecture Room C

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