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}
}
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4 Citations
Highly Influential Citations
1
Background Citations
2

4 Citations

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Lectures on geometric realizations of crystals
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References

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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.
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