TY - JOUR

T1 - Double Schubert polynomials for the classical groups

AU - Ikeda, Takeshi

AU - Mihalcea, Leonardo C.

AU - Naruse, Hiroshi

N1 - Funding Information:
* Corresponding author. E-mail addresses: ike@xmath.ous.ac.jp (T. Ikeda), Leonardo_Mihalcea@baylor.edu (L.C. Mihalcea), rdcv1654@cc.okayama-u.ac.jp (H. Naruse). 1 T. Ikeda was partially supported by Grant-in-Aid for Scientific Research (C) 20540053.

PY - 2011/1/15

Y1 - 2011/1/15

N2 - For each infinite series of the classical Lie groups of type B, C or D, we construct a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. They are also positive in a certain sense, and when indexed by maximal Grassmannian elements, or by the longest element in a finite Weyl group, these polynomials can be expressed in terms of the factorial analogues of Schur's Q- or P-functions defined earlier by Ivanov.

AB - For each infinite series of the classical Lie groups of type B, C or D, we construct a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. They are also positive in a certain sense, and when indexed by maximal Grassmannian elements, or by the longest element in a finite Weyl group, these polynomials can be expressed in terms of the factorial analogues of Schur's Q- or P-functions defined earlier by Ivanov.

KW - Double Schubert polynomials

KW - Equivariant cohomology

KW - Factorial P or Q-Schur

UR - http://www.scopus.com/inward/record.url?scp=77958484993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958484993&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2010.07.008

DO - 10.1016/j.aim.2010.07.008

M3 - Article

AN - SCOPUS:77958484993

VL - 226

SP - 840

EP - 886

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -