Elliptic analogue of Vershik-Kerov limit shape

Abstract

We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and uniform measure, a U(1) case of N=2* gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric ``arcsin'' law of Vershik-Kerov and Logan-Schepp.

19 pages, contribution to Functional Analysis volume dedicated to the 90th anniversary of Anatoly Moiseevich Vershik