Critical points of master functions and flag varieties

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 $s{l}_{N+1},s{o}_{2N+1}$, and $s{p}_{2N}$. We show that populations associated with a collection of integral dominant $s{l}_{N+1}$-weights are in one to one correspondence with intersection points of suitable Schubert cycles in a Grassmannian variety.

Latex, 49 pages