University of Toronto's Symplectic Geometry Seminar

Nov. 8 2004, 1:10 - 2

Greg Landweber

University of Oregon and Fields Institute

"Twisted representation rings and Dirac induction"

Abstract: We begin by introducing the twisted equivariant K-theory of a point, the twisted representation ring, built from projective representations of a compact Lie group with a given cocycle. We then extend this definition to construct twisted representation rings for Lie supergroups. As an application, given a compact Lie group, we can consider its parity reversed tangent bundle as a Lie supergroup, whose representation ring agrees with that of the original group via a Thom isomorphism. If we have a Lie subgroup H of maximal rank inside a compact Lie group G, then we show that the induction map from the representation ring of TH to that of TG is in fact the Dirac induction map from R(H) to R(G).