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Generalized Green functions and graded Hecke algebras

K. Slooten
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Abstract

We state a conjecture which gives a combinatorial parametrization of the irreducible tempered representations with real central character of a graded Hecke algebra with unequal labels, associated to a root sytem of type B or C. This conjecture is based on a combinatorial generalization of the Springer correspondence in the classical (equal label) case. In particular, the described modules turn out to have a natural grading for the action of W_0, and are completely determined by their central character together with the W_0-representation in the top degree. This latter is an irreducible W_0-character which we call Springer correspondent.

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K. Slooten. 2004-04-09. Generalized Green functions and graded Hecke algebras. https://arxiv.org/abs/math/0404202

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