Dominant K-theory and integrable highest weight representations of Kac–Moody groups

Kitchloo, Nitu

doi:10.1016/j.aim.2009.02.006

Cited by 19 publications

(21 citation statements)

References 23 publications

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“…Together with the isomorphism R(H) ∼ = K 0 G (G/H), the result above shows that the induction map as defined in this paper, can be identified in K-theory as the push-forward along the map obtained by composing G/H → e → G. For this side of the story, see also [8,14].…”

Section: Corollary 46 For Any Equal Rank Inclusion H ⊂ G Dirac Indmentioning

confidence: 92%

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Dirac Induction for Loop Groups

Posthuma

2010

Lett Math Phys

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Section: Corollary 46 For Any Equal Rank Inclusion H ⊂ G Dirac Indmentioning

confidence: 92%

“…The same homomorphism can be constructed topologically in equivariant (twisted) K-theory, cf. [4], see also [3,8,14].…”

Section: Introductionmentioning

confidence: 99%

Dirac Induction for Loop Groups

Posthuma

2010

Lett Math Phys

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“…15 We say that a G-map A f −→ X is a cofibration if it satisfies the homotopy extension property with respect to all G-spaces Y and G-homotopies. That is, given any G-map g 0 : X → Y and a G-homotopy H :…”

Section: Definition 44 a Local Quotient Groupoid Is A Groupoidmentioning

confidence: 99%

Twisted K-theory for actions of Lie groupoids and its completion theorem

Cantarero

2010

Math. Z.

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In this paper we define twisted equivariant K -theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid G, we show that this defines a periodic cohomology theory on the category of finite G-CW-complexes with G-stable projective bundles by comparing with a suitable representable cohomology theory. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.

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“…It arose originally in the work of Freed, Hopkins, and Teleman, though only a related spectral sequence in K-cohomology appears in their papers. It has been described explicitly by Meinrenken [16] and is discussed by Kitchloo and Morava [13,14].…”

Section: Here C S Denotes the Barycenter Of The Face Of The Weyl Alcomentioning

confidence: 99%

“…2.3 we reformulate the equivariant spectral sequence in terms of "twisted representation modules", that is in terms of modules of representations of central extensions of subgroups of G, and we express the d 1 differentials of the spectral sequence as twisted holomorphic induction maps between these modules. The resulting resolution of the fusion ring is implicit in the work of Freed, Hopkins, and Teleman, is described in papers of Kitchloo and Morava [13,14], and is presented in detail from the point of view of the twisted K-theory of C * -algebras by Meinrenken [16]. The reader already familiar with this resolution of the fusion ring may want to turn directly to the results of Sect.…”

Section: Introductionmentioning

confidence: 99%