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Hecke algebras with unequal parameters and Vogan’s left cell invariants

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Representations of Reductive Groups

Part of the book series: Progress in Mathematics ((PM,volume 312))

Abstract

In 1979, Vogan introduced a generalised τ-invariant for characterising primitive ideals in enveloping algebras. Via a known dictionary this translates to an invariant of left cells in the sense of Kazhdan and Lusztig. Although it is not a complete invariant, it is extremely useful in describing left cells. Here, we propose a general framework for defining such invariants which also applies to Hecke algebras with unequal parameters.

To David Vogan on the occasion of his 60th birthday

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Acknowledgements

The first author is partly supported by the ANR (Project No. ANR-12-JS01-0003-01 ACORT). The second author is partly supported by DFG Priority Programme SPP 1489.

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Authors and Affiliations

  1. Institut de Mathématiques et de Modélisation de Montpellier (CNRS: UMR 5149), Université Montpellier 2, Case Courrier 051, Place Eugène Bataillon, 34095, Montpellier Cedex, France

    Cédric Bonnafé

  2. Fachbereich Mathematik, IAZ - Lehrstuhl für Algebra, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Meinolf Geck

Authors
  1. Cédric Bonnafé
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  2. Meinolf Geck
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Correspondence to Meinolf Geck .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada

    Monica Nevins

  2. Dept of Mathematics and Statistics, University of Utah, Salt Lake City, Utah, USA

    Peter E. Trapa

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Bonnafé, C., Geck, M. (2015). Hecke algebras with unequal parameters and Vogan’s left cell invariants. In: Nevins, M., Trapa, P. (eds) Representations of Reductive Groups. Progress in Mathematics, vol 312. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23443-4_6

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