Raising Operators for the Whittaker Wave Functions of the Toda Chain and Intertwining Operators

Whittaker Functions on Quantum Groups and Q-deformed Toda Operators

Let G be a simply connected simple Lie group over C. Let N± be the positive and the negative maximal unipotent subgroups, and H the maximal torus, corresponding to some polarization of G. Let G0 = N−HN+ be the big Bruhat cell. Let χ± : N± → C be holomorphic nondegenerate characters (i.e. they don’t vanish on simple roots). A Whittaker function on G0 with characters χ+, χ− is any holomorphic fun...

On Baxter Q-operators for Toda Chain

We suggest the procedure of the construction of Baxter Q-operators for Toda chain. Apart from the one-paramitric family of Q-operators, considered in our recent paper [4] we also give the construction of two basic Q-operators and the derivation of the functional relations for these operators. Also we have found the relation of the basic Q-operators with Bloch solutions of the quantum linear pro...

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 ...

Intertwining Operators and Residues

Young raising operators and Q-functions

A number of properties of Young raising operators as applied to S-functions and Schur Q-functions are noted. The order of evaluating the action of inverse raising operators is found to require careful specification and the maximum power of the operators bij is determined. The operation of the inverse raising operator on a partition .A is found to be the same as for its conjugate t A new definit...