# Generalized Green functions and graded Hecke algebras

Source: [Generalized Green functions and graded Hecke algebras](<https://www.sota2.com/research/paper/68fa4cd91e209131ce94fa17>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T08:59:21.930Z

Authors: K. Slooten

Published: 2004-04-09T15:11:04.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0404202>)

[PDF](<https://arxiv.org/pdf/math/0404202.pdf>)