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Push-pull operators on the formal affine Demazure algebra and its dual

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Abstract

In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal affine Demazure algebra which serves as an algebraic counterpart of the natural pairing on the equivariant oriented cohomology of the complete flag variety induced by multiplication and push-forward to a point.

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Acknowledgements

One of the ingredients of this paper, the push-pull formulas in the context of Weyl group actions, arose in discussions between the first author and Victor Petrov, whose unapparent contribution we therefore gratefully acknowledge.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Lens, Université d’Artois, Arras, France

    Baptiste Calmès

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Kirill Zainoulline

  3. Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA

    Changlong Zhong

Authors
  1. Baptiste Calmès
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  2. Kirill Zainoulline
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  3. Changlong Zhong
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Corresponding author

Correspondence to Kirill Zainoulline.

Additional information

The first author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. The second author was supported by the NSERC Discovery grant 385795-2010, NSERC DAS Grant 396100-2010 and the Early Researcher Award (Ontario). The third author was supported by PIMS and the NSERC grants of Vladimir Chernousov and Stefan Gille. We appreciate the support of the Fields Institute; part of this work was done while authors were attending the Thematic Program on Torsors, Nonassociative algebras and Cohomological Invariants at the Fields Institute.

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Calmès, B., Zainoulline, K. & Zhong, C. Push-pull operators on the formal affine Demazure algebra and its dual. manuscripta math. 160, 9–50 (2019). https://doi.org/10.1007/s00229-018-1058-4

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  • DOI: https://doi.org/10.1007/s00229-018-1058-4

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