CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Involutions in finite special orthogonal groups C. Ryan Vinroot, College of William and Mary
March 8, 2011 Math 220 2-3pm	Abstract Let I(n) denote the number of elements whose square is the identity in SO(n,q), a special orthogonal group over a field with q elements. The topic of this talk is the fact that the sequence I(n) is semi-recursive in n, in that I(2m+3) depends on I(2m+1) and I(2m-2) linearly. The combinatorial proof of this fact brings to light mysterious equalities between the number of involutions in various finite classical groups. I will also give an application of this semi-recursion for I(n) to give a universal bound for the character degree sum for finite classical groups over fields of odd characteristic. This work is joint work with Feiqi Jiang, an undergraduate from the University of Michigan.

Involutions in finite special orthogonal groups

C. Ryan Vinroot, College of William and Mary

March 8, 2011

Math 220

2-3pm

Abstract

Let I(n) denote the number of elements whose square is the identity in SO(n,q), a special orthogonal group over a field with q elements. The topic of this talk is the fact that the sequence I(n) is semi-recursive in n, in that I(2m+3) depends on I(2m+1) and I(2m-2) linearly. The combinatorial proof of this fact brings to light mysterious equalities between the number of involutions in various finite classical groups. I will also give an application of this semi-recursion for I(n) to give a universal bound for the character degree sum for finite classical groups over fields of odd characteristic. This work is joint work with Feiqi Jiang, an undergraduate from the University of Michigan.