Publication Date
2003
Journal or Book Title
COMPTES RENDUS MATHEMATIQUE
Abstract
We construct Nakajima's quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disjoint union of quiver varieties. Consequently, singularities of quiver varieties, nilpotent orbits and affine Grassmannians are the same in type A. The construction also provides a geometric framework for skew (GL(m),GL(n)) duality and identifies the natural basis of weight spaces in Nakajima's construction with the natural basis of multiplicity spaces in tensor products which arises from affine Grassmannians. To cite this article: I. Mirkovi , M. Vybornov, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Pages
207-212
Volume
336
Issue
3
Recommended Citation
Mirkovic, I and Vybornov, M, "On quiver varieties and affine Grassmanians of type A" (2003). COMPTES RENDUS MATHEMATIQUE. 729.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/729
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X1B-480630X-2&_user=1516330&_coverDate=02%2F01%2F2003&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1663892867&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=c22a3d32bc67663448067abc2c186f12&searchtype=a