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Critical points of master functions and flag varieties

E. Mukhin·A. Varchenko
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Abstract

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.

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E. Mukhin, A. Varchenko. 2002-09-02. Critical points of master functions and flag varieties. https://arxiv.org/abs/math/0209017

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