Abstract

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.

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