How to regularize singular vectors and kill the dynamical Weyl group

Details How to regularize singular vectors and kill the dynamical Weyl group How to regularize singular vectors and kill the dynamical Weyl group

2002-06-27

arxiv.org/abs/math/0206294v1

Mathematics

Quantum Algebra

35 pages, AMSLaTeX

Scientific paper

We study the meromorphic family of intertwining operators between Verma modules and their products with finite-dimensional ones. A regularizing operator, acting in a finite dimensional module U, makes this family holomorphic, and conjugates the dynamical Weyl group operators to constant operators. We prove uniqueness property for regularizing operators, and construct them explicitly for the Lie algebra sl_3.

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