Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, 100:45

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

  • V Lakshmibai
  • B Sandhya
Article

DOI: 10.1007/BF02881113

Cite this article as:
Lakshmibai, V. & Sandhya, B. Proc. Indian Acad. Sci. (Math. Sci.) (1990) 100: 45. doi:10.1007/BF02881113

Abstract

LetG=Sl(n) andB, the Borel subgroup ofG consisting of upper triangular matrices. LetwSn 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.

Keywords

Schubert varietysmoothness, geometric criterion

Copyright information

© Indian Academy of Sciences 1990

Authors and Affiliations

  • V Lakshmibai
    • 1
  • B Sandhya
    • 2
  1. 1.Mathematics DepartmentNortheastern UniversityBostonUSA
  2. 2.Institute of Mathematical SciencesMadrasIndia
  3. 3.School of MathematicsSPIC Science FoundationMadrasIndia