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The equivariant cohomology of weighted flag orbifolds

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Abstract

We describe the torus-equivariant cohomology of weighted partial flag orbifolds \({\mathrm {w}}\Sigma \) 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 \({\mathrm {w}}\Sigma \) ”. For the weighed Schubert classes in \({\mathrm {w}}\Sigma \), 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.

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Acknowledgements

We wish to thank Waqar Ali Shah for several helpful discussions. We also thank Frank Sottile and Balázs Szendrői for their comments on earlier drafts of this article. Thanks are also due to Shizu Kaji, Allen Knutson and Loring Tu for some useful conversations. Last but not least, we are indebted to the anonymous referee for his/her comments and suggestions which significantly improved the earlier version of this paper. HA and MIQ were supported by the HEC’s NRPU research grant “5906/Punjab/NRPU/R&D/HEC/2016”. MIQ was on a fellowship of Alexander–Von–Humboldt foundation during a part of this paper.

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Authors and Affiliations

  1. Department of Mathematics, SBASSE, Lahore University of Management Sciences (LUMS), Lahore, Pakistan

    Haniya Azam, Shaheen Nazir & Muhammad Imran Qureshi

  2. Mathematisches Institut, Universität Tübingen, Tübingen, Germany

    Muhammad Imran Qureshi

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  1. Haniya Azam
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  2. Shaheen Nazir
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  3. Muhammad Imran Qureshi
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Correspondence to Muhammad Imran Qureshi.

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Azam, H., Nazir, S. & Qureshi, M.I. The equivariant cohomology of weighted flag orbifolds. Math. Z. 294, 881–900 (2020). https://doi.org/10.1007/s00209-019-02285-x

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