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AFLT-type Selberg integrals
Seamus P. Albion, Eric M. Rains, S. Ole Warnaar
In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for a Selberg integral over the product of two Jack polyn…
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…
A Fuchsian matrix differential equation for Selberg correlation integrals
Peter J. Forrester, Eric M. Rains
We characterize averages of with respect to the Selberg density, further contrained so that and $(l=q+…
On Algebraically Integrable Differential Operators on an Elliptic Curve
Pavel Etingof, Eric Rains
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of or…
Matrix averages relating to the Ginibre ensembles
Peter J. Forrester, Eric M. Rains
The theory of zonal polynomials is used to compute the average of a Schur polynomial of argument , where is a fixed matrix and is from the real Ginibre ensemble. This g…
q-Distributions on boxed plane partitions
Alexei Borodin, Vadim Gorin, Eric M. Rains
We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box.…