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EQUIVARIANT QUANTUM SCHUBERT POLYNOMIALS DAVE ANDERSON AND LINDA CHEN
 

Summary: EQUIVARIANT QUANTUM SCHUBERT POLYNOMIALS
DAVE ANDERSON AND LINDA CHEN
Abstract. We establish an equivariant quantum Giambelli formula for
partial flag varieties. The answer is given in terms of a specialization
of universal double Schubert polynomials. Along the way, we give new
proofs of the presentation of the equivariant quantum cohomology ring,
as well as Graham-positivity of the structure constants in equivariant
quantum Schubert calculus.
1. Introduction
Classical Schubert calculus is concerned with the cohomology rings of
Grassmannians and (partial) flag varieties. In recent years, equivariant and
quantum versions of Schubert calculus have been developed. Key ingredients
in each of these theories are a presentation of the ring and a "Giambelli
formula" expressing the additive basis of Schubert classes in terms of the
presentation. For example, the ordinary cohomology of the Grassmannian
is generated by Chern classes, and the classical Giambelli formula in this
context states that a Schubert class is represented by a Schur polynomial
and gives a determinantal expression for these polynomials in terms of Chern
classes.
The past fifteen years have seen great progress in modern Schubert cal-

  

Source: Anderson, Dave - Department of Mathematics, University of Washington at Seattle

 

Collections: Mathematics