$(gl_n, gl_m)$ -对偶的拉格朗日构造
Lagrangian construction of the $(gl_n, gl_m)$-duality
摘要：
给出了张量空间$C^n \bigotimes C^m$的对称代数的几何实现以及对偶对$(gl_n, gl_m)$在某些簇的余切丛中的拉格朗日圈的作用.在几何上建立了$(gl_n, gl_m)$对偶与Schur对偶的等价性.我们建立了Springer构造外尔群（表示）和Ginzburg构造$A$型李代数（表示）之间的联系。
英文摘要：
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 $A$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
