On Quiver Varieties and Affine Grassmannians of Type A
نویسندگان
چکیده
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. Dedicated to Igor Frenkel on the occasion of his 50-th birthday
منابع مشابه
Quiver Varieties and Beilinson-drinfeld Grassmannians of Type A
We construct Nakajima’s quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy’s) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima’s quiver varieties and a decomposition of an affine Grassmannian i...
متن کاملHomological Approach to the Hernandez-leclerc Construction and Quiver Varieties
In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver...
متن کاملQuiver Grassmannians, Quiver Varieties and the Preprojective Algebra
Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective ...
متن کاملQuiver varieties and Frenkel-Kac construction
An affine Lie algebra acts on cohomology groups of quiver varieties of affine type. A Heisenberg algebra acts on cohomology groups of Hilbert schemes of points on a minimal resolution of a Kleinian singularity. We show that in the case of type A the former is obtained by Frenkel-Kac construction from the latter.
متن کاملBases of Representations of Type a Affine Lie Algebras via Quiver Varieties and Statistical Mechanics
We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics that also respects the weight space decomposition of the representations. In particular, we are able to give an alternative and much simpler geometric proof of the main r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002