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Demazure character formula for semi-infinite flag varieties

  • Syu Kato
Article
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Abstract

We prove that every Schubert variety of a semi-infinite flag variety is projectively normal. This gives us an interpretation of a Demazure module of a global Weyl module of a current Lie algebra as the (dual) space of global sections of a line bundle on a semi-infinite Schubert variety. Moreover, we give geometric realizations of Feigin–Makedonskyi’s generalized Weyl modules, and the \(t = \infty \) specialization of non-symmetric Macdonald polynomials.

Notes

Acknowledgements

The author would like to thank Michael Finkelberg for attracting his attention to [16] and sent me his unpublished note [4]. He also would like to thank Satoshi Naito for various comments and suggestions on the topic presented in this paper, Shrawan Kumar for discussion on semi-infinite flag varieties, and Evgeny Feigin and Daniel Orr for preventing him from some incorrect references. The original version of this paper was written during the author’s stay at MIT in the academic year 2015/2016. The author would like to thank George Lusztig and MIT for their hospitality. Finally, the author would like to express his thanks to the referee who have kindly made many remarks on the previous version of this paper.

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Copyright information

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

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan

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