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

Character deflations, wreath products and Foulkes' Conjecture

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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 then the permutation character of the symmetric group Sab acting on set partitions of a set of size ab into b sets each of size a contains the permutation character of Sab 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 Sa with Sb to characters of Sb. 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.

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