The equivariant cohomology of weighted flag orbifolds

Haniya Azam; Shaheen Nazir; Muhammad Imran Qureshi

doi:10.1007/s00209-019-02285-x

The equivariant cohomology of weighted flag orbifolds

Haniya Azam, Shaheen Nazir, Muhammad Imran Qureshi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We describe the torus-equivariant cohomology of weighted partial flag orbifolds w Σ of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as “Schubert Calculus on w Σ ”. For the weighed Schubert classes in w Σ , we give the Chevalley’s formula. In addition, we define the weighted analogue of double Schubert polynomials and give the corresponding Chevalley–Monk’s formula.

Original language	English
Pages (from-to)	881-900
Number of pages	20
Journal	Mathematische Zeitschrift
Volume	294
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-019-02285-x
State	Published - 1 Apr 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Double Schubert polynomials
Equivariant cohomology
Schubert classes
Weighted flag varieties

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-019-02285-x

Cite this

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title = "The equivariant cohomology of weighted flag orbifolds",

abstract = "We describe the torus-equivariant cohomology of weighted partial flag orbifolds w Σ of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as “Schubert Calculus on w Σ ”. For the weighed Schubert classes in w Σ , we give the Chevalley{\textquoteright}s formula. In addition, we define the weighted analogue of double Schubert polynomials and give the corresponding Chevalley–Monk{\textquoteright}s formula.",

keywords = "Double Schubert polynomials, Equivariant cohomology, Schubert classes, Weighted flag varieties",

author = "Haniya Azam and Shaheen Nazir and Qureshi, \{Muhammad Imran\}",

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N2 - We describe the torus-equivariant cohomology of weighted partial flag orbifolds w Σ of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as “Schubert Calculus on w Σ ”. For the weighed Schubert classes in w Σ , we give the Chevalley’s formula. In addition, we define the weighted analogue of double Schubert polynomials and give the corresponding Chevalley–Monk’s formula.

AB - We describe the torus-equivariant cohomology of weighted partial flag orbifolds w Σ of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as “Schubert Calculus on w Σ ”. For the weighed Schubert classes in w Σ , we give the Chevalley’s formula. In addition, we define the weighted analogue of double Schubert polynomials and give the corresponding Chevalley–Monk’s formula.

KW - Double Schubert polynomials

KW - Equivariant cohomology

KW - Schubert classes

KW - Weighted flag varieties

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JF - Mathematische Zeitschrift

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ER -

The equivariant cohomology of weighted flag orbifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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