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Schur Q-Functions and Degeneracy Locus Formulas for Morphisms with Symmetries

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Recent Progress in Intersection Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle and is based on a push-forward formula for these polynomials in a Grassmann bundle, established in [P4].

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Authors and Affiliations

  1. C.N.R.S. Institut Gaspard Monge, Université de Marne-la-Vallée, 5 Bd Descartes, Champs sur Marne, Marne La Vallée Cedex 2, 77454, France

    Alain Lascoux

  2. Mathematical Institute of Polish Academy of Sciences, Chopina 12, Toruń, 87-100, Poland

    Piotr Pragacz

Authors
  1. Alain Lascoux
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  2. Piotr Pragacz
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oslo, N-0316, Oslo, Sweden

    Geir Ellingsrud

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    William Fulton

  3. Departimento di Matematica, Università di Bologna, Bologna, 40127, Italy

    Angelo Vistoli

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Lascoux, A., Pragacz, P. (2000). Schur Q-Functions and Degeneracy Locus Formulas for Morphisms with Symmetries. In: Ellingsrud, G., Fulton, W., Vistoli, A. (eds) Recent Progress in Intersection Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1316-1_8

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  • DOI: https://doi.org/10.1007/978-1-4612-1316-1_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7090-4

  • Online ISBN: 978-1-4612-1316-1

  • eBook Packages: Springer Book Archive

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