Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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 Al(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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