Vanishing of one dimensional L^2-cohomologies of loop groups

Details Vanishing of one dimensional L^2-cohomologies of loop groups Vanishing of one dimensional L^2-cohomologies of loop groups

2011-08-29

arxiv.org/abs/1108.5564v1

Journal of Functional Analysis, Vol.261, issue 8, page 2164-2213, 2011

Mathematics

Probability

Scientific paper

10.1016/j.jfa.2011.06.003

Let $G$ be a simply connected compact Lie group. Let $L_e(G)$ be the based loop group with the base point $e$ which is the identity element. Let $\nu_e$ be the pinned Brownian motion measure on $L_e(G)$ and let $\alpha\in L^2(\wedge^1T^{\ast}L_e(G),\nu_e)\cap {\mathbb D}^{\infty,p}(\wedge^1T^{\ast}L_e(G),\nu_e)$ $(1

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