Martin boundaries of the duals of free unitary quantum groups

Abstract

Given a free unitary quantum group $G=A_u(F)$, with $F$ not a unitary $2$-by-$2$ matrix, we show that the Martin boundary of the dual of $G$ with respect to any $G$-$\hat{G}$-invariant, irreducible, finite range quantum random walk coincides with the topological boundary defined by Vaes and Vander Vennet. This can be thought of as a quantum analogue of the fact that the Martin boundary of a free group coincides with the space of ends of its Cayley tree.

18 pages; v2: minor corrections

References in corpus (3)

• Orientation of quantum Cayley trees and applications
• Categorical duality for Yetter-Drinfeld algebras
• Poisson boundaries of monoidal categories

Cited by in corpus (1)

• Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles