## Generating varieties for affine Grassmannians

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- by Peter J. Littig and Stephen A. Mitchell
- Trans. Amer. Math. Soc.
**363**(2011), 3717-3731 - DOI: https://doi.org/10.1090/S0002-9947-2011-05257-8
- Published electronically: January 11, 2011
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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 $G_2$.## References

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## Bibliographic 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
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 3717-3731 - MSC (2000): Primary 14M15; Secondary 57T99, 55P35
- DOI: https://doi.org/10.1090/S0002-9947-2011-05257-8
- MathSciNet review: 2775825