Hua type beta-integrals and projective systems of measures on flag spaces

TL;DR

This paper constructs a family of compatible measures on flag spaces, leading to a multi-parameter family of beta-integrals over upper-triangular matrices, advancing the understanding of measure systems in geometric and algebraic contexts.

Contribution

It introduces a new family of measures on flag spaces compatible with projections, and derives a multi-parameter family of beta-integrals on upper-triangular matrices.

Findings

Established a compatible measure system on flag spaces.

Derived an explicit multi-parameter family of beta-integrals.

Connected measure constructions with classical integral formulas.

Abstract

We construct a family of measures on flag spaces (or, equivalently, on the spaces of upper-triangular matrices) compatible with respect to natural projections. We obtain an $n(n-1)/2$-parametric family of beta-integrals over space of upper-triangular matrices of size $n$.