Critical points of master functions and flag varieties

By E. Mukhin, A. Varchenko. 2002

106 citations recorded by the source corpus.

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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ac1ebbd81dc17366f4fdc40e8af854d765120c4f

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In Discrete Mathematics and Combinatorics

1. V. Tarasov
2. E. Mukhin
3. A. Varchenko

In Geometry and Topology

1. V. Tarasov
2. A. Varchenko
3. E. Mukhin
4. Valerio Toledano Laredo
5. P. Boalch
6. Alexandre Eremenko
7. Andrei Gabrielov

In Mathematical Physics

1. V. Tarasov
2. E. Mukhin
3. A. Varchenko

Citations in the corpus

• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz (2005, methodology): “The value ω(t; z) of the universal weight function at a critical point t of the master function �( � ; z) is called a Bethe vector, see [RV, MV2 ].”