Pieri integral formula and asymptotics of Jack unitary characters

@article{Cuenca2017PieriIF,
title={Pieri integral formula and asymptotics of Jack unitary characters},
author={Cesar Cuenca},
journal={Selecta Mathematica},
year={2017},
volume={24},
pages={2737-2789}
}

We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations for Jack characters of one variable. The second identity we prove is the Pieri integral formula for Jack characters which, in a sense, is dual to the well known Pieri rule for Jack polynomials. The Pieri integral formula can also be seen as a functional… CONTINUE READING