The isospectrality problem is studied for the operator of the spherical hydromagnetic α−dynamo. It is shown that this operator is formally pseudo-Hermitian (J−symmetric) and lives in a Krein space. Based on the J−symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the α−dynamo operator matrix. An in...

Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for ŝl(2) satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection with Gordon’s generalization of the Rogers–Ramanujan identities and with Andrews’ related ide...

The trace of intertwining operators over the level one irreducible highest weight modules of the quantum affine algebra of type AN−1 is studied. It is proved that the trace function gives a basis of the solution space of the qKZ equation at a generic level. The highest-highest matrix element of the composition of intertwining operators is explicitly calculated. The integral formula for the trac...

The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.

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...