Representations of Algebraic Groups

04/21/2015 - 12:15pm
04/21/2015 - 1:10pm
Eric Friedlander (University of Southern California)

We consider affine algebraic groups G over a field k and rational (i.e., algebraic) actions of G on k-vector spaces V. We seek to provide some understanding of such actions through examples, algebraic invariants, and geometric structures. Our first example of an algebraic group is the general linear group GL_N, but we shall primarily focus on the example of the additive group G_a over k of characteristic p > 0. The representation theory of G_a is far too complicated to fully classify, but sufficiently accessible to reveal considerable structure. Our efforts lead to finite subgroup schemes of G_a and finite dimensional sub-coalgebras of the algebraic functions k[G_a] = k[T].

Mudd Science Library 126, Pomona College

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