| The heat kernel measure nut is constructed on W (G), the group of paths based at the identity on a simply connected complex Lie group G. An isometric map, the Taylor map, is established from the space of L2(nu t)-holomorphic functions on W (G) to a subspace of the dual of the universal enveloping algebra of Lie(H(G)), where H( G) is the Lie subgroup of finite energy paths. Surjectivity of this Taylor map can be shown in the case where G is stratified nilpotent. |
