Skip to main content
SpringerLink
Log in

COTANGENT BUNDLE TO THE FLAG VARIETY–I

  • Published:
Transformation Groups Aims and scope Submit manuscript

Abstract

We show that there is a SLn-stable closed subset of an affine Schubert variety in the infinite-dimensional flag variety (associated to the Kac-Moody group \( \widehat{{\mathrm{SL}}_n} \)) which is a natural compactification of the cotangent bundle to the finite-dimensional flag variety SLn/B.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Achar, A. Henderson Geometric Satake, Springer correspondence, and small representations, Selecta Math. 19 (2013), 949–986.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Achar, A. Henderson, S. Riche Geometric Satake, Springer correspondence, and small representations II, Represent. Theory 19 (2015), 94–166.

    Article  MathSciNet  MATH  Google Scholar 

  3. V. Kac, Infinite Dimensional Lie Algebras, Cambridge University Press, Cambridge, 1990

    Book  MATH  Google Scholar 

  4. S. Kumar, Kac-Moody Groups, their Flag Varieties and Representation Theory, Progress in Mathematics, Vol. 204, Birkhäuser Boston, Boston, MA, 2002.

  5. V. Lakshmibai, Cotangent bundle to the Grassmann variety, Transform. Groups 21 (2016), no. 2, 519–530.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Lakshmibai, C. S. Seshadri, Geometry of G/P-II, Proc. Ind. Acad. Sci. 87A (1978), 1–54.

    MATH  Google Scholar 

  7. V. Lakshmibai, V. Ravikumar, W. Slofstra, Cotangent bundle of a cominuscule Grassmannian, Michigan Math. J. 65 (2016), 749–759.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. Math. 42 (1981), no. 2, 169–178.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447–498.

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Manivel, M. Michalek, Secants of minuscule and cominuscule minimal orbits, Linear Algebra Appl. 481 (2015), 288–312.

    Article  MathSciNet  MATH  Google Scholar 

  11. I. Mirkovic, M. Vybornov, On quiver varieties and affine Grassmannians of type A, C. R. Math. Acad. Sci. Paris 336 (2003), no. 3, 207–212.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Strickland, On the conormal bundle of the determinantal variety, J. Algebra 75 (1982), 523–537.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    V. LAKSHMIBAI & R. SINGH

  2. Chennai Mathematical Institute, Siruseri, Kelambakkam, Chennai, Tamil Nadu, 603103, India

    C. S. SESHADRI

Authors
  1. V. LAKSHMIBAI
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. S. SESHADRI
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. SINGH
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. LAKSHMIBAI.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

LAKSHMIBAI, V., SESHADRI, C.S. & SINGH, R. COTANGENT BUNDLE TO THE FLAG VARIETY–I. Transformation Groups 24, 127–147 (2019). https://doi.org/10.1007/s00031-017-9466-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00031-017-9466-1

Search

Navigation