Higher Lame Equations and Critical Points of Master Functions

2006/01/29 by E. Mukhin, Mukhin, E., V. Tarasov +4
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #math.CA

paper · pdf · doi:10.48550/arxiv.math/0601703

Latex, 11 pages, revised version

openalex publication_date 2006/01/29 · arxiv created 2006/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \glg_r+1.

Citations

• Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model

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