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Mirabolic affine Grassmannian and character sheaves

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Abstract.

We compute the Frobenius trace functions of mirabolic character sheaves defined over a finite field. The answer is given in terms of the character values of general linear groups over the finite field, and the structure constants of multiplication in the mirabolic Hall–Littlewood basis of symmetric functions, introduced by Shoji.

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Authors and Affiliations

  1. Mathematics Department, rm. 517, IMU, IITP and State University Higher School of Economy, 20 Myasnitskaya st., Moscow, 101000, Russia

    Michael Finkelberg

  2. Mathematics Department, University of Chicago, Chicago, IL, 60637, USA

    Victor Ginzburg

  3. Mathematics Department, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Roman Travkin

Authors
  1. Michael Finkelberg
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  2. Victor Ginzburg
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  3. Roman Travkin
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Correspondence to Michael Finkelberg.

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Finkelberg, M., Ginzburg, V. & Travkin, R. Mirabolic affine Grassmannian and character sheaves. Sel. math., New ser. 14, 607–628 (2009). https://doi.org/10.1007/s00029-009-0509-x

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  • DOI: https://doi.org/10.1007/s00029-009-0509-x

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