Skip to main content
SpringerLink
Log in

Schubert Quiver Grassmannians

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincaré polynomials of these quiver Grassmannians.

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. Cerulli Irelli, G., Lanini, M.: Degenerate flag varieties of type A and C are Schubert varieties. IMRN 15, 6353–6374 (2015) arXiv:1403.2889

    Article  MathSciNet  MATH  Google Scholar 

  2. Cerulli Irelli, G., Lanini, M., Littelmann, P.: Degenerate flag varieties and Schubert varieties: a characteristic free approach. arXiv:1502.04590. To appear in Pacific Journal of Mathematics (2016)

  3. Cerulli Irelli, G., Feigin, E., Reineke, M.: Quiver Grassmannians and degenerate flag varieties. Algebra & Number Theory 6(1), 165–194 (2012) [arXiv:1106.2399]

    Article  MathSciNet  MATH  Google Scholar 

  4. Cerulli Irelli, G., Feigin, E., Reineke, M.: Degenerate flag varieties: moment graphs and Schröder numbers. J. Algebraic Combin. 138 (1) (2013). arXiv:1206.4178

  5. Feigin, E.: \(\mathbb {G}_{a}^{M}\) degeneration of flag varieties. Selecta Mathematica New Series 18(3), 513–537 (2012)

  6. Feigin, E.: Degenerate flag varieties and the median Genocchi numbers. Mathematical Research Letters 18(6), 1–16 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fulton, W.: Young Tableaux. London Mathematical Society Student Texts, vol. 35. Cambridge University Press, Cambridge (1997)

  8. Haupt, N.: Euler Characteristic and Geometric Properties of Quiver Grassmannians. Ph.D Thesis, University of Bonn (2011)

  9. Möllenhoff, K., Reineke, M.: Embeddings of representations. Algebr. Represent. Theory. 18, 977–987 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Giovanni Cerulli Irelli

  2. Department of Mathematics, National Research University Higher School of Economics, Vavilova str. 7, 117312, Moscow, Russia

    Evgeny Feigin

  3. Tamm Department of Theoretical Physics, Lebedev Physics Institute, Moscow, Russia

    Evgeny Feigin

  4. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraβe 150, D-44780, Bochum, Germany

    Markus Reineke

Authors
  1. Giovanni Cerulli Irelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evgeny Feigin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markus Reineke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Cerulli Irelli.

Additional information

Presented by Michel Brion.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cerulli Irelli, G., Feigin, E. & Reineke, M. Schubert Quiver Grassmannians. Algebr Represent Theor 20, 147–161 (2017). https://doi.org/10.1007/s10468-016-9634-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10468-016-9634-3

Keywords

Mathematics Subject Classification (2010)

Search

Navigation