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Beilinson–Drinfeld Schubert varieties and global Demazure modules

Part of: Special varieties Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  25 May 2021

Ilya Dumanski ,
Evgeny Feigin  and
Michael Finkelberg
Ilya Dumanski
Affiliation:
Department of Mathematics, HSE University, Usacheva str. 6, Moscow, 119048, Russia Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, Moscow, 119002, Russia; E-mail: ilyadumnsk@gmail.com
Evgeny Feigin*
Affiliation:
Department of Mathematics, HSE University, Usacheva str. 6, Moscow, 119048, Russia Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Building 3, Moscow, 143026, Russia; E-mail: evgfeig@gmail.com
Michael Finkelberg
Affiliation:
Department of Mathematics, HSE University, Russia, Usacheva str. 6, Moscow, 119048, Russia Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Building 3, Moscow, 143026, Russia Institute for Information Transmission Problems of RAS, Moscow, Russia; E-mail: fnklberg@gmail.com
*
Email: evgfeig@gmail.com

Abstract

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We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.

MSC classification

Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Type
Algebra
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e42
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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