Critical points of master functions and flag varieties
Critical points of master functions and flag varieties
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主函数和标志品种的关键点
DOI：
10.1142/s0219199704001288
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
A. Varchenko
中科院分区：
文献类型：
--
作者：
E. Mukhin;A. Varchenko
We consider critical points of master functions associated with integral dominant weights of Kac-Moody algebras and introduce a generating procedure constructing new critical points starting from a given one. The set of all critical points constructed from a given one is called a population. We formulate a conjecture that a population is isomorphic to the flag variety of the Langlands dual Kac-Moody algebra and prove the conjecture for algebras $sl_{N+1}, so_{2N+1}$, and $sp_{2N}$.
We show that populations associated with a collection of integral dominant $sl_{N+1}$-weights are in one to one correspondence with intersection points of suitable Schubert cycles in a Grassmannian variety.
