Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 10
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Wyser, Benjamin J. 2016. K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles splitting as direct sums. Geometriae Dedicata, Vol. 181, Issue. 1, p. 137.


    Ikeda, Takeshi and Matsumura, Tomoo 2015. Pfaffian sum formula for the symplectic Grassmannians. Mathematische Zeitschrift, Vol. 280, Issue. 1-2, p. 269.


    Pon, Steven 2012. Affine Stanley symmetric functions for classical types. Journal of Algebraic Combinatorics, Vol. 36, Issue. 4, p. 595.


    CHEONG, DAEWOONG 2011. VAFA-INTRILIGATOR TYPE FORMULAS AND QUANTUM EULER CLASSES FOR LAGRANGIAN AND ORTHOGONAL GRASSMANNIANNS. International Journal of Algebra and Computation, Vol. 21, Issue. 04, p. 575.


    Ikeda, Takeshi Mihalcea, Leonardo C. and Naruse, Hiroshi 2011. Double Schubert polynomials for the classical groups. Advances in Mathematics, Vol. 226, Issue. 1, p. 840.


    Tamvakis, Harry 2011. Schubert polynomials and Arakelov theory of orthogonal flag varieties. Mathematische Zeitschrift, Vol. 268, Issue. 1-2, p. 355.


    Tamvakis, Harry 2011. Giambelli, Pieri, and tableau formulas via raising operators. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2011, Issue. 652,


    Duan, Haibao Zhao, Xu-an and Zhao, Xuezhi 2004. The Cartan matrix and enumerative calculus. Journal of Symbolic Computation, Vol. 38, Issue. 3, p. 1119.


    Kirillov, Anatol N. and Maeno, Toshiaki 2004. Noncommutative algebras related with Schubert calculus on Coxeter groups. European Journal of Combinatorics, Vol. 25, Issue. 8, p. 1301.


    Lascoux, Alain and Pragacz, Piotr 1998. Operator Calculus forQ̃-Polynomials and Schubert Polynomials. Advances in Mathematics, Vol. 140, Issue. 1, p. 1.


    ×

Formulas for Lagranigian and orthogonal degeneracy loci; $\tilde{Q}$-polynomial approach

  • P. PRAGACZ (a1) and J. RATAJSKI (a2)
  • DOI: http://dx.doi.org/10.1023/A:1000182205320
  • Published online: 01 May 1997
Abstract

The main goal of the paper is to give explicit formulas for the fundamental classes of Schubert subschemes in Lagrangian and orthogonal Grassmannians of maximal isotropic subbundles as well as some globalizations of them. The used geometric tools overlap appropriate desingularizations of such Schubert subschemes and Gysin maps for such Grassmannian bundles. The main algebraic tools are provided by the families of $\tilde{Q}$- and $\tilde{P}$-polynomials introduced and investigated in the present paper. The key technical result of the paper is the computation of the class of the (relative) diagonal in isotropic Grassmannian bundles based on the orthogonality property of $\tilde{Q}$- and $\tilde{P}$-polynomials. Some relationships with quaternionic Schubert varieties and Schubert polynomials for classical groups are also discussed.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Formulas for Lagranigian and orthogonal degeneracy loci; $\tilde{Q}$-polynomial approach
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Formulas for Lagranigian and orthogonal degeneracy loci; $\tilde{Q}$-polynomial approach
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Formulas for Lagranigian and orthogonal degeneracy loci; $\tilde{Q}$-polynomial approach
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: