Integration formulas for Brownian motion on classical compact Lie groups

TL;DR

This paper derives combinatorial formulas for the moments of Brownian motion on classical compact Lie groups, connecting stochastic calculus with invariant theory and Schur-Weyl dualities.

Contribution

It provides new combinatorial formulas for Brownian motion moments that deform known Haar measure formulas, linking stochastic calculus with classical invariant theory.

Findings

Derived combinatorial formulas for Brownian motion moments.

Proved the First Fundamental Theorem of invariant theory using stochastic calculus.

Connected Brownian motion on Lie groups with Schur-Weyl dualities.

Abstract

Combinatorial formulas for the moments of the Brownian motion on classical compact Lie groups are obtained. These expressions are deformations of formulas of B. Collins and P. \'Sniady for moments of the Haar measure and yield a proof of the First Fundamental Theorem of invariant theory and of classical Schur-Weyl dualities based on stochastic calculus.