Residues of Intertwining Operators for Classical Groups

Intertwining Operators and Residues

Intertwining operators and residues II. Invariant distributions

1. Residues . ..... ........ .... ... .... 54 2. ir-discrete distributions ............... . .. . . .. . 58 3. Admissible families of operators .......... ............. 67 4. The main formula ............. ... ............ 74 5. Completion of the induction argument .................... 83 6. Cuspidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Conclusions ..............

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...

Traces of intertwining operators and

Traces of intertwining operators and Macdonald's polynomials Alexander A. Kirillov, Jr. May 1995 Let : V ! V U be an intertwining operator between representations of a simple Lie algebra (quantum group, a ne Lie algebra). We de ne its generalized character to be the following function on the Cartan subalgebra with values in U : (h) = TrV ( eh). This is a generalization of usual characters. Thes...

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1)a, of central charge 1 − 12a . We classify these operators in terms of depth and provide explicit constructions ...