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Journal of Lie Theory 22 (2012), No. 4, 1149--1168
Copyright Heldermann Verlag 2012

Wrapping Brownian Motion and Heat Kernels. I: Compact Lie Groups

David G. Maher
Market Risk, Wholesale Banking, National Australia Bank, L2/88 Wood Street, London EC2V 7QQ, England

An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel.

Keywords: Compact Lie group, Brownian motion, wrapping map.

MSC: 43A77, 22E30, 58J65

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