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 Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• School of Mathematics events
• Watson Building, Lecture Room C

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