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Generating varieties for affine Grassmannians

Authors: Peter J. Littig and Stephen A. Mitchell
Journal: Trans. Amer. Math. Soc. 363 (2011), 3717-3731
MSC (2000): Primary 14M15; Secondary 57T99, 55P35
Published electronically: January 11, 2011
MathSciNet review: 2775825
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Abstract: We study Schubert varieties that generate the affine Grassmannian under the loop group product, and in particular generate the homology ring. There is a canonical such Schubert generating variety in each Lie type. The canonical generating varieties are not smooth, and in fact smooth Schubert generating varieties exist only if the group is not of type $ E_8$, $ F_4$ or $ G_2$.

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Additional Information

Peter J. Littig
Affiliation: Science and Technology Program, University of Washington, Bothell, Box 358258, Bothell, Washington 98011

Stephen A. Mitchell
Affiliation: Department of Mathematics 354352, University of Washington, Seattle, Washington 98195

Received by editor(s): November 18, 2008
Received by editor(s) in revised form: November 20, 2009
Published electronically: January 11, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.