Dirac Induction for Loop Groups

Posthuma, Hessel

doi:10.1007/s11005-010-0453-x

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…It has now been generalized to infinite-dimensional case and plays an important role in the theory of loop groups: its application in representation theory was first demonstrated in the lecture notes of Wassermann [Was10]. Later Landweber and Posthuma generalize it to different homogeneous settings [Lan01,Pos11]. A family version of the cubic Dirac operator was used by Freed-Hopkins-Teleman [FHT13] to construct the isomorphism between the twisted K-theory and fusion ring of loop groups.…”

Section: Dirac Operators In the Algebraic Settingmentioning

confidence: 99%

Dirac operators on quasi-Hamiltonian G-spaces

Song

2015

Preprint

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We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi-Hamiltonian G-spaces, using the spin representation of loop group and the Hilbert space of Wess-Zumino-Witten model. We then define a Hilbert space together with a Dirac operator acting on it. The main result of this paper is that we show the Dirac operator has a welldefined index given by positive energy representation of loop group. This generalizes the geometric quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces.

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Section: Dirac Operators In the Algebraic Settingmentioning

confidence: 99%

Dirac operators on quasi-Hamiltonian G-spaces

Song

2015

Preprint

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“…Remark 5.7. Landweber [20] and Posthuma [31] generalized the construction of relative cubic Dirac operators to the loop group setting, in which they obtained different generalizations of the Weyl-Kac formula.…”

Section: Let Dmentioning

confidence: 99%

A K-homological approach to the quantization commutes with reduction problem

Song

2014

Preprint

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In [15], Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product of C * -algebras. Then we define the quantization of Hamiltonian G-spaces as a push-forward of the Dirac element. With this, we develop a K-homological approach to the quantization commutes with reduction theorem.

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Dirac operators on quasi-Hamiltonian G-spaces

Song

2016

Journal of Geometry and Physics

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Dirac Induction for Loop Groups

Cited by 4 publications

References 18 publications

Dirac operators on quasi-Hamiltonian G-spaces

Dirac operators on quasi-Hamiltonian G-spaces

A K-homological approach to the quantization commutes with reduction problem

Dirac operators on quasi-Hamiltonian G-spaces

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