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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…
An elliptic Garnier system
Christopher M. Ormerod, Eric M. Rains
We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at points for , which a…
The noncommutative geometry of elliptic difference equations
Eric M. Rains
We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a 1-parameter noncommutative deformation to any projective rational surface with…
Vector bundles on genus 2 curves and trivectors
Eric M. Rains, Steven V Sam
Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic.…
A symmetric difference-differential Lax pair for Painlevé VI
Christopher M. Ormerod, Eric M. Rains
We present a Lax pair for the sixth Painlevé equation arising as a continuous isomonodromic deformation of a system of linear difference equations with an additional symmetry struc…
Abelian varieties isogenous to a power of an elliptic curve
Bruce W. Jordan, Allan G. Keeton, Bjorn Poonen +3
Let be an elliptic curve over a field . Let . There is a functor from the category of finitely presented torsion-free…