Character formulæ and GKRS multiplets in equivariant K-theory

Details Character formulæ and GKRS multiplets in equivariant K-theory Character formulæ and GKRS multiplets in equivariant K-theory

2011-07-18

arxiv.org/abs/1107.3578v1

Mathematics

K-Theory and Homology

37 pages

Scientific paper

Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $K_H^*(X)$ viewed as a module over the $G$-equivariant K-ring $K_G^*(X)$. One result is that the module has a nonsingular bilinear pairing; another is that the module contains multiplets which are analogous to the Gross-Kostant-Ramond-Sternberg multiplets of representation theory. We also obtain a Borel-Weil-Bott theorem on the induction of irreducible representations of $H$.

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