Frobenius-Schur indicator of a self-dual representation of GL(n,F_q)
event Friday, April 21, 2023
access_time 3:45pm (CDT)
room PHSC 1105
free_breakfast Tea at 3:15pm (CDT) in PHSC 424
Abstract: Given an irreducible complex representation (R,V) of a finite group G, Frobenius and Schur, around 1900, introduced an invariant for answering the question of when R is real, that is, when there is a basis of V such that the associated matrix of R(g) has real entries for all g in G. The invariant, now known as the Frobenius-Schur indicator, is difficult to compute directly. By an argument of D. Prasad, however, it is given in many cases by the action of a certain central element which is easy to compute. We will outline Prasad's method focusing mostly on the case of GL(n, F), F a finite field.
For more information on this event, please contact Travis Mandel.