Global character formulae for compact Lie groups

Abstract

Abstract. We introduce the concept of a modulator, which leads to a family of character formulae, each generalizing the Kirillov formula. For a suitable choice of modulator, this enables one to understand the Plancherel measure of a compact Lie group as arising from a partition of the identity on the dual of its Lie algebra.

Wrapping Brownian motion and heat kernels II: symmetric spaces

“…where j is smooth and real valued. Taking µ = j, by [14] Prop. 2.4, we have Φ(j) = 1, and so Φ(L p j + (∆ Y e(X, 0) − (L p j)(0))j) = L G/K 1 = 0 and thus j −1 L p j = (L p j)(0) − ∆ Y e(X, 0) which concludes the proof.…”