Combinatorics Seminar-Generating functions for induced characters of the hyperoctahedral group

Speaker: MarkSkandera, Lehigh University
Date and time: Wednesday, February 19, 4:00–5:00pm
Place: Rome 204
Title: Generating functions for induced characters of the hyperoctahedral group

Abstract:  Merris and Watkins interpreted results of Littlewood to give generating functions for symmetric group characters induced from one-dimensional characters of Young subgroups. Beginning with an n by n matrix X of formal variables, one obtains induced sign and trivial characters by expanding sums of products of certain determinants and permanents, respectively. We will look at a new analogous result which holds for hyperoctahedral group characters induced from the four one-dimensional characters of its Young subgroups. This requires a 2n by 2n matrix of formal variables and four combinations of determinants and permanents. This is joint work with Jongwon Kim.