Mathematical Sciences Seminar - Character deflations, wreath products and Foulkes' Conjecture
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
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 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 this 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 characters. I will explain how this rule may be used to compute the irreducible constituents of Foulkes characters, and show that our result is a simultaneous generalization of both Young's rule and the Murnaghan–Nakayama rule on characters of symmetric groups.
This talk is on joint work with Anton Evseev (Birmingham) and Rowena Paget (Kent).
Contact name:
Department of Economics, Mathematics and Statistics