A Duistermaat–Heckman type formula for the based loop group

Jack Ding and Lisa Jeffrey ()
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Jack Ding: University of Toronto
Lisa Jeffrey: University of Toronto

Partial Differential Equations and Applications, 2022, vol. 3, issue 4, 1-16

Abstract: Abstract We generalize work done by Picken (J Math Phys 31:616–638, 1990). We give a generalization of the Duistermaat–Heckman formula for oscillatory integrals on the based loop group G by using the Wiener measure. Previously work has been done by Wendt for the generic coadjoint orbit LG/T; we carry out a similar computation for the degenerate coadjoint orbit $$LG/ G \cong \Omega G$$ L G / G ≅ Ω G .

Keywords: Loop groups; Oscillatory integral localization; Primary 22E65; 53D50; Secondary (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00192-1

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