167 citations · 1.9k across the 134 of their papers we have counts for
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Potentials of a family of arrangements of hyperplanes and elementary subarrangements
Andrew Prudhom, Alexander Varchenko
We consider the Frobenius algebra of functions on the critical set of the master function of a weighted arrangement of hyperplanes in $\C^k$ with normal crossings. We construct two…
Affine Macdonald conjectures and special values of Felder-Varchenko functions
Eric M. Rains, Yi Sun, Alexander Varchenko
We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr. and prove the first non-trivial cases of the…
Potentials of a Frobenius like structure and bases of a vector space
Claus Hertling, Alexander Varchenko
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. Surprisingly the pro…
Cyclotomic discriminantal arrangements and diagram automorphisms of Lie algebras
Alexander Varchenko, Charles A. S. Young
Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, we identify a class of affi…
On axioms of Frobenius like structure in the theory of arrangements
Alexander Varchenko
A Frobenius manifold is a manifold with a flat metric and a Frobenius algebra structure on tangent spaces at points of the manifold such that the structure constants of multiplicat…