Yuri A. Neretin
Double Cosets for $SU(2)\times\dots\times SU(2)$ and Outer Automorphisms of Free Groups
The paper is published: Int. Math. Res. Notes 2011, 2047-2067

MSC:

16W20 Automorphisms and endomorphisms, actions of groups and semigroups and their fixed rings

20F36 Braid groups; Artin groups

20E05 Free nonabelian groups

Abstract: Consider the space of double cosets of
the product of $n$ copies of $\SU(2)$ with respect to the diagonal
subgroup. We get a parametrization
of this space, the radial part of the Haar measure,
and explicit formulas for the actions of the group of outer
automorphisms of the free group $F_{n-1}$
and of the braid group of $n-1$ strings.


Keywords: invariants, braid group, Haar measure, free group, outer automorphisms of free group