Representations of the Symplectic groups Sp(4,2^t) and the Suzuki groups, with applications.
Dr. Peter Sin
University of Florida

Abstract:

Let $k$ be an algebraic closure of GF(2). The algebraic group Sp(4,k) has an endomorphism $\tau$ whose square is the Frobenius map. This endomorphism has a construction by projective geometry, the groups of fixed points of the powers of $\tau$ are the finite groups Sp(4,2^t) and the Suzuki groups. Moreover, $\tau$ is very helpful for parametrizing the irreducible representations of these groups.

In this talk, I will survey these constructions and the related computation of the extension groups $Ext1_G(V,W)$ between simple modules. Finally, the application of this theory to the computation of 2-ranks for the generalized quadrangle W(2^t) and related geometries will be described, ending with some open questions