# The Duistermaat–Heckman distribution for the based loop group

### APA

Jeffrey, L. (2018). The Duistermaat–Heckman distribution for the based loop group . Perimeter Institute. https://pirsa.org/18080056

### MLA

Jeffrey, Lisa. The Duistermaat–Heckman distribution for the based loop group . Perimeter Institute, Aug. 14, 2018, https://pirsa.org/18080056

### BibTex

@misc{ pirsa_PIRSA:18080056, doi = {10.48660/18080056}, url = {https://pirsa.org/18080056}, author = {Jeffrey, Lisa}, keywords = {Mathematical physics}, language = {en}, title = { The Duistermaat{\textendash}Heckman distribution for the based loop group }, publisher = {Perimeter Institute}, year = {2018}, month = {aug}, note = {PIRSA:18080056 see, \url{https://pirsa.org}} }

University of Toronto

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Abstract

The based loop group is an inﬁnite-dimensional manifold equipped with a Hamiltonian action of a ﬁnite dimensional torus. This was studied by Atiyah and Pressley. We investigate the Duistermaat–Heckman distribution using the theory of hyperfunctions. In applications involving Hamiltonian actions on inﬁnite-dimensional manifolds, this theory is necessary to accommodate the existence of the inﬁnite order diﬀerential operators which aries from the isotropy representation on the tangent spaces to ﬁxed points. (Joint work with James Mracek)