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Hecke algebras and involutions in Coxeter groups

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Representations of Reductive Groups

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

Abstract

Let W be a Coxeter group and let M be the free Z[v, v −1]-module with basis indexed by the involutions of W. We show how the recent results of Elias and Williamson on Soergel bimodules can be used to give an alternative definition of an action of the Hecke algebra of W on M​.

The first author dedicates this paper to the second author and wishes him many productive years

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References

  1. B. Elias and G. Williamson, The Hodge theory of Soergel bimodules, Ann. Math. 180 (2014), 1089–1136.

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Acknowledgements

This research supported in part by National Science Foundation grants DMS-1303060 and DMS-0967272.

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Authors and Affiliations

  1. Department of Mathematics, M.I.T., Cambridge, MA, 02139, USA

    George Lusztig & David A. Vogan Jr.

Authors
  1. George Lusztig
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  2. David A. Vogan Jr.
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Corresponding author

Correspondence to George Lusztig .

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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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Lusztig, G., Vogan, D.A. (2015). Hecke algebras and involutions in Coxeter groups. 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_13

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