Lagrangian construction of the $(gl_n, gl_m)$-duality
Representation Theory
2007-05-23 v2 Algebraic Geometry
Abstract
We give a geometric realization of the symmetric algebra of the tensor space together with the action of the dual pair in terms of lagrangian cycles in the cotangent bundles of certain varieties. We establish geometrically the equivalence between the duality and Schur duality. We establish the connection between Springer's construction of (representations of) Weyl groups and Ginzburg's construction of (representations of) Lie algebras of type .
Keywords
Cite
@article{arxiv.math/9907154,
title = {Lagrangian construction of the $(gl_n, gl_m)$-duality},
author = {Weiqiang Wang},
journal= {arXiv preprint arXiv:math/9907154},
year = {2007}
}
Comments
14 pages,latex, minor changes, to appear in Communications in Contemporary Mathematics