Miura Opers and Critical Points of Master Functions

2003/12/22 by E. Mukhin, Evgeny Mukhin, Mukhin, Evgeny +2
Arts and Humanities · Mathematics · #FOS: Mathematics #Musicology and Musical Analysis #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0312406

Latex, 27 pages

openalex publication_date 2003/12/22 · arxiv created 2004/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \g^t. The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population.

Citations

• Self-self-dual spaces of polynomials

Cited by

• Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras

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