Generating functions for induced characters of the hyperoctahedral group

Algebra Seminar
Monday, March 9, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Mark Skandera – Lehigh University
Greg Blekherman

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.