#### 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.

Done