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

  • Baptiste Calmès
  • Kirill Zainoulline
  • Changlong Zhong
Article
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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.

Mathematics Subject Classification

20C08 14F43 57T15 

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Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de LensUniversité d’ArtoisArrasFrance
  2. 2.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  3. 3.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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