Abstract

Under certain conditions, we give an estimate from above on the number of differential equations of order r + 1 with prescribed regular singular points, prescribed exponents at singular points, and having a quasi-polynomial flag of solutions. The estimate is given in terms of a suitable weight subspace of the tensor power U(n−) ⊗(n−1) , where n is the number of singular points in C and U(n−) is the enveloping algebra of the nilpotent subalgebra of glr+1.

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