Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 1569–1603 | Cite as

Equivariant quantum cohomology of the odd symplectic Grassmannian

  • Leonardo C. Mihalcea
  • Ryan M. ShiflerEmail author


The odd symplectic Grassmannian \(\mathrm {IG}:=\mathrm {IG}(k, 2n+1)\) parametrizes k dimensional subspaces of \({\mathbb {C}}^{2n+1}\) which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on \(\mathrm {IG}\) with two orbits, and \(\mathrm {IG}\) is itself a smooth Schubert variety in the submaximal isotropic Grassmannian \(\mathrm {IG}(k, 2n+2)\). We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of \(\mathrm {IG}\), i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case \(k=2\), and it gives an algorithm to calculate any multiplication in the equivariant quantum cohomology ring.

Mathematics Subject Classification

Primary 14N35 Secondary 14N15 14M15 



We would like to thank Dan Orr and Mark Shimozono for discussions and valuable suggestions and to Pierre-Emmanuel Chaput, Changzheng Li, and Nicolas Perrin for discussions and collaborations on related projects. Special thanks are due to Anders Buch for encouragement and interest in this project. We thank the referee for carefully reading our paper.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Mathematics, 460 McBryde HallVirginia TechBlacksburgUSA
  2. 2.Department of Mathematics and Computer Science, Henson Science HallSalisbury UniversitySalisburyUSA

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