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Criterion for smoothness of Schubert varieties in Sl(n)/B

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Abstract

LetG=Sl(n) andB, the Borel subgroup ofG consisting of upper triangular matrices. Letw∈S n andX(w)=BwB(modB), the associated Schubert variety inG/B. In this paper, we give a geometric criterion for the smoothness ofX(w). This criterion admits a neat combinatorial description in terms of the permutationw.

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Author notes

  1. B Sandhya

    Present address: School of Mathematics, SPIC Science Foundation, No. 92, GN Chetty Road, T. Nagar, 600 017, Madras, India

Authors and Affiliations

  1. Mathematics Department, Northeastern University, 02115, Boston, Ma., USA

    V Lakshmibai

  2. Institute of Mathematical Sciences, 600 113, Madras, India

    B Sandhya

Authors
  1. V Lakshmibai
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  2. B Sandhya
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Lakshmibai, V., Sandhya, B. Criterion for smoothness of Schubert varieties in Sl(n)/B . Proc. Indian Acad. Sci. (Math. Sci.) 100, 45–52 (1990). https://doi.org/10.1007/BF02881113

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  • DOI: https://doi.org/10.1007/BF02881113

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