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Toroidal Schubert Varieties

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Abstract

Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the toroidal and horospherical partial flag varieties with Picard number 1. In the more general case, we provide a set of necessary conditions for the action of a Levi subgroup on a Schubert variety to be toroidal. The singular locus of a (co)minuscule Schubert variety is shown to contain all the Lmax-stable Schubert subvarieties, where Lmax is the standard Levi subgroup of the maximal parabolic which acts on the Schubert variety by left multiplication. In type A, the effect of the Billey-Postnikov decomposition on toroidal Schubert varieties is obtained.

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Acknowledgments

The first author is partially supported by a grant from the Louisiana Board of Regents. We are grateful to the referee whose comments helped us to see and fix our mistakes; this greatly improved the quality of our paper.

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Authors and Affiliations

  1. Tulane University, New Orleans, LA, USA

    Mahir Bilen Can

  2. The University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Reuven Hodges

  3. Northeastern University, Boston, MA, USA

    Venkatramani Lakshmibai

Authors
  1. Mahir Bilen Can
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  2. Reuven Hodges
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  3. Venkatramani Lakshmibai
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Correspondence to Mahir Bilen Can.

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Presented by: Peter Littelmann

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Can, M.B., Hodges, R. & Lakshmibai, V. Toroidal Schubert Varieties. Algebr Represent Theor 23, 1927–1943 (2020). https://doi.org/10.1007/s10468-019-09921-4

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  • DOI: https://doi.org/10.1007/s10468-019-09921-4

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