SIGMA 5 (2009), 048, 31 pages      arXiv:0809.2081      https://doi.org/10.3842/SIGMA.2009.048
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Singularities of Affine Schubert Varieties

Jochen Kuttler ^a and Venkatramani Lakshmibai ^b
a) Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, Canada
^b) Department of Mathematics, Northeastern University, Boston, USA

Received September 11, 2008, in final form April 03, 2009; Published online April 18, 2009

Abstract
This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type A_l⁽¹⁾). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.

Key words: Schubert varieties; affine Grassmannian; loop Grassmannian.

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