关于GL（n）表示的Ginzburg Lagrange构造
On Ginzburg's Lagrangian construction of representations of GL(n)
摘要：
在1991年，V. Ginzburg观察到人们可以在GL（d）群的某些Springer纤维的上同调中实现群$GL(n,C)$的不可约表示（对于所有自然d）。然而，Ginzburg对GL（n）在这个上同调上的作用的构造有点人为（他根据A. Beilinson，G. Lusztig和R. MacPherson给出了量子群$U_q(gl(n))$的类似构造）。本文给出了整个群GL（n，C）在上述上同调上作用的一个非常简单的几何定义，并简化了Ginzburg的结果。
英文摘要：
In 1991 V. Ginzburg observed that one can realize irreducible representations of the group $GL(n,C)$ in the cohomology of certain Springer's fibers for the group GL(d) (for all natural d). However, Ginzburg's construction of the action of GL(n) on this cohomology was a bit artificial (he defined the action of Chevalley generators of the Lie algebra gl(n) on the corresponding cohomology by certain explicit correspondences, following the work of A. Beilinson, G. Lusztig and R. MacPherson, who gave a similar construction of the quantum group $U_q(gl(n))$). In this note we give a very simple geometric definition of the action of the whole group GL(n,C) on the above cohomology and simplify the Ginzburg's results.
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