Global functional calculus for operators on compact Lie groups

-bounds for Pseudo-differential Operators on Compact Lie Groups

Given a compact Lie group G, in this paper we establish L p-bounds for pseudo-differential operators in L p(G). The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space G× Ĝ, where Ĝ is the unitary dual of G. We obtain two different types of L p bounds: first for finite regularity symbols and second for smooth symbols. The c...

Global Character Formulae for Compact Lie Groups

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.

Dirac Operators for Coadjoint Orbits of Compact Lie Groups

The coadjoint orbits of compact Lie groups carry many Kähler structures, which include a Riemannian metric and a complex structure. We provide a fairly explicit formula for the Levi–Civita connection of the Riemannian metric, and we use the complex structure to give a fairly explicit construction of the Dirac operator for the Riemannian metric, in a way that avoids use of the spin groups. Subst...

Invariant Differential Operators for Non-Compact Lie Groups: Parabolic Subalgebras

In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalised to the supersymmetric and quantum group sett...

Probability on Compact Lie Groups