On two geometric constructions of U( sl n ) and its representations

@article{Savage2006OnTG,
  title={On two geometric constructions of U( sl n ) and its representations},
  author={Alistair Savage},
  journal={Journal of Algebra},
  year={2006},
  volume={305},
  pages={664-686}
}

Figures from this paper

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

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

Lectures on geometric realizations of crystals

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

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

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

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

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

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

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

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 $GL_n$

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

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

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