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Double theta polynomials and equivariant Giambelli formulas

Published online by Cambridge University Press:  18 December 2015

HARRY TAMVAKIS  and
ELIZABETH WILSON
HARRY TAMVAKIS
Affiliation:
University of Maryland, Department of Mathematics, 1301 Mathematics Building, College Park, MD 20742, U.S.A. e-mail: harryt@math.umd.edu; bethmcl@math.umd.edu
ELIZABETH WILSON
Affiliation:
University of Maryland, Department of Mathematics, 1301 Mathematics Building, College Park, MD 20742, U.S.A. e-mail: harryt@math.umd.edu; bethmcl@math.umd.edu
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Abstract

We use Young's raising operators to introduce and study double theta polynomials, which specialize to both the theta polynomials of Buch, Kresch, and Tamvakis, and to double (or factorial) Schur S-polynomials and Q-polynomials. These double theta polynomials give Giambelli formulas which represent the equivariant Schubert classes in the torus-equivariant cohomology ring of symplectic Grassmannians, and we employ them to obtain a new presentation of this ring in terms of intrinsic generators and relations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 2 , March 2016 , pp. 353 - 377
Copyright
Copyright © Cambridge Philosophical Society 2015 

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