We compute natural integrals giving intertwining operators among principal series of G = SL(2, C).

We show that if every module W for a vertex operator algebra V = ∐ n∈Z V(n) satisfies the condition dimW/C1(W ) < ∞, where C1(W ) is the subspace of W spanned by elements of the form u−1w for u ∈ V+ = ∐ n>0 V(n) and w ∈W , then matrix elements of products and iterates of intertwining operators satisfy certain systems of differential equations. Moreover, for prescribed singular points, there exi...

These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable particle systems of Calogero-MoserSut...

The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel relating little q-Jacobi function transforms for different parameter sets. A product formula for the dual transmutation kernel is obtained. For the inverse transform the transmutation kernel is given as a 3φ2-series, ...

Following the procedure, described in the paper [9], for the integrable DST chain we construct Baxter Q-operators [1] as the traces of monodromy of some M-operators, that act in quantum and auxiliary spaces. Within this procedure we obtain two basic M-operators and derive some functional relations between them such as intertwining relations and wronskian-type relations between two basic Q-opera...

In this paper we prove the absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual. Next we present some applications of this result. Key word : Dunkl intertwining operator and its dual. Absolute continuity of the representing measures. MSC (2000) : 33C80, 51F15, 44A15. Introduction We consider the differential-difference operators on R introduced by ...