Degenerate Double Affine Hecke Algebra and Conformal Field Theory

We introduce a class of induced representations of the degenerate double affine Hecke algebra H of $$g{l_N}$$(ℂ) and analyze their structure mainly by means of intertwiners of H. We also construct them from $$\hat s{l_m}$$(ℂ)-modules using Knizhnik-Zamolodchikov connections in the conformai field theory. This construction provides a natural quotient of induced modules, which turns out to be the unique irreducible one under a certain condition. Some conjectural formulas are presented for the symmetric part of these quotients.