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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Generating varieties for affine Grassmannians
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by Peter J. Littig and Stephen A. Mitchell PDF
Trans. Amer. Math. Soc. 363 (2011), 3717-3731 Request permission


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
  • © 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:
  • MathSciNet review: 2775825