Alladi Ramakrishnan Hall

Conjugation orbits of semisimple pairs in rank one

Krishnendu Gongopadhyay

IISER Mohali

 We consider the Lie group G= SU(n,1), resp. Sp(n,1), that acts by
the isometries of the n-dimensional complex, resp. quaternionic hyperbolic
space. We classify pairs of semisimple elements in G up to conjugacy.  This
gives local parametrization of a representation $\rho$ in Hom(F_2, G)/G such
that both $\rho(x)$ and $\rho(y)$ are semisimple elements, where $F_2$ is a
free group generated by x and y.