Lagrangian construction of the $(gl_n, gl_m)$-duality

Weiqiang Wang

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Lagrangian construction of the (gl_n, gl_m)-duality

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arxiv math/9907154 v2 pith:L7BTCBDK submitted 1999-07-23 math.RT math.AG

Lagrangian construction of the (gl_n, gl_m)-duality

Weiqiang Wang This is my paper

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We give a geometric realization of the symmetric algebra of the tensor space $C^n \bigotimes C^m$ together with the action of the dual pair $(gl_n, gl_m)$ in terms of lagrangian cycles in the cotangent bundles of certain varieties. We establish geometrically the equivalence between the $(gl_n, gl_m)$ 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 $A$.

Lagrangian construction of the (gl_n, gl_m)-duality

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