In this paper, a comparison between the Bergman kernel form and pushforward measure of Masur-Veech on Teichmüller space genus g ≥ 2 <mml:annotation encoding...

Let = G=K be a bounded symmetric domain in a complex vector space V with the Lebesgue measure dm(z) and the Bergman reproducing kernel h(z; w) ?p. Let dd (z) = h(z; z) dm(z), > ?1, be the weighted measure on. The group G acts unitarily on the space L 2 ((;) via change of variables together with a multiplier. We consider the discrete parts, also called the relative discrete series, in the irredu...