## Figures from this paper

## 4 Citations

### QUIVER VARIETIES AND BEILINSON-DRINFELD GRASSMANNIANS OF TYPE A

- Mathematics
- 2008

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…

### Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A

- MathematicsAdvances in Mathematics
- 2022

### Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities

- MathematicsAdvances in Mathematics
- 2021

### Lectures on geometric realizations of crystals

- Mathematics
- 2010

These are notes for a lecture series given at the Fields Institute Summer School in Geometric Representation Theory and Extended Affine Lie Algebras, held at the University of Ottawa in June 2009. We…

## References

SHOWING 1-10 OF 14 REFERENCES

### Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras

- Mathematics
- 1994

To Professor Shoshichi Kobayashi on his 60th birthday 1. Introduction. In this paper we shall introduce a new family of varieties, which we call quiver varieties, and study their geometric…

### Geometric construction of crystal bases

- Mathematics
- 1996

We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As…

### Quiver varieties and tensor products

- Mathematics
- 2001

Abstract.In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety &?tilde; in a quiver…

### Tensor product varieties and crystals. ADE case

- Mathematics
- 2001

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These…

### Tensor product varieties and crystals. GL case

- Mathematics
- 2001

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These…

### Introduction to Quantum Groups

- Mathematics
- 1993

THE DRINFELD JIMBO ALGERBRA U.- The Algebra f.- Weyl Group, Root Datum.- The Algebra U.- The Quasi--Matrix.- The Symmetries of an Integrable U-Module.- Complete Reducibility Theorems.- Higher Order…

### Crystal bases and quiver varieties

- Mathematics
- 2002

Abstract. We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One can show that, as a crystal, it is isomorphic to the crystal base of…

### Relation between two geometrically defined bases in representations of $GL_n$

- Mathematics
- 2004

Let $V$ be an irreducible representation of group $GL_n({\mathbb C})$, which appears as a submodule in $({\mathbb C}^n)^{\otimes d}$, where ${\mathbb C}^n$ is the tautological $n$-dimensional…

### Quiver varieties of type A

- Mathematics
- 1998

We prove a conjecture of Nakajima describing the relation between quiver varieties of type A and the geometry of partial flag varieties and of the nilpotent variety

### Representation theory and complex geometry

- Mathematics, Biology
- 1997

This book discusses K-Theory, Symplectic Geometry, Flag Varieties, K- theory, and Harmonic Polynomials, and Representations of Convolution Algebras.