Generalized Green functions and graded Hecke algebras

2004/04/09 by K. Slooten, Slooten, K.
Mathematics · #05E99 #20C08 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E99 #msc:20C08

paper · pdf · doi:10.48550/arxiv.math/0404202

59 pages, 15 figures

arxiv created 2004/04/09 · openalex publication_date 2004/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 W₀, and are completely determined by their central character together with the W₀-representation in the top degree. This latter is an irreducible W₀-character which we call Springer correspondent.

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