Decomposition of $C\sp{\infty }$ intertwining operators for Lie groups

Functional Equations Satisfied by Intertwining Operators of Reductive Groups

This paper generalizes a recent work of Vogan and Wallach [VW] in which they derived a difference equation satisfied by intertwining operators of reductive groups. We show that, associated with each irreducible finitedimensional representation, there is a functional equation relating intertwining operators. In this way, we obtain natural relations between intertwining operators for different se...

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...

Intertwining Operators and Residues

Operators on Diierential Forms for Lie Transformation Groups

For any Lie group action S: GP ! P , we introduce C 1 (P)

-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...