2002/09/02 by E. Mukhin, Mukhin, E., Alexander Varchenko +2
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0209017
Latex, 49 pages
arxiv created 2002/09/02 · openalex publication_date 2002/09/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 slN+1, so2N+1, and sp2N. We show that populations associated with a collection of integral dominant slN+1-weights are in one to one correspondence with intersection points of suitable Schubert cycles in a Grassmannian variety.