Generating functions and statistics on spaces of maximal tori in classical Lie groups

Jason Fulman, Rita Rolland, Jennifer Wilson
2017 New York Journal of Mathematics New York J. Math   unpublished
In this paper we use generating function methods to obtain new asymptotic results about spaces of F-stable maximal tori in GLn(Fq), Sp 2n (Fq), and SO2n+1(Fq). We recover stability results of Church-Ellenberg-Farb and Jiménez Rolland-Wilson for "polynomial" statistics on these spaces, and we compute explicit formulas for their stable values. We derive a double generating function for the characters of the cohomology of flag varieties in type B/C, which we use to obtain analogs in type B/C of
more » ... ults of Chen: we recover "twisted homological stability" for the spaces of maximal tori in Sp 2n (C) and SO2n+1(C), and we compute a generating function for their "stable twisted Betti num-bers". We also give a new proof of a result of Lehrer using symmetric function theory.