#### IMSc Webinar

#### Generating Functions for Involutions and Character Degree Sums in Finite Groups of Lie Type

#### Ryan Vinroot

##### William and Mary

*Webinar link: us02web.zoom.us/j/85402825387*

Given a finite group G, it is a result of Frobenius and Schur that all complex irreducible representations of G may be defined over the reals if and only if the character degree sum of G is equal to the number of involutions of G. We use this result and generatingfunctionology to study the real representations of finite groups of Lie type, and to obtain some new combinatorial identities. We will begin with examples of Weyl groups, then discuss joint work with Jason Fulman on finite general linear and unitary groups, and then give more recent results for finite symplectic and orthogonal groups.

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