Title: Deforming Representations of SL(2,R),
Abstract: The spherical principal series representations $\pi(\nu)$ of SL(2,$\mathbb
R$) is a family of infinite dimensional representations parametrized by
$\nu\in\mathbb C$. The representation $\pi(\nu)$ is irreducible unless $\nu$ is
an odd integer, in which case it is indecomposable. We find a new continuous
family of representations $\Pi(\nu)$ such that $\pi(\nu)$ and $\Pi(\nu)$ have
the same composition factors, and $\Pi(\nu)$ is completely reducible, for all
$\nu$. We also describe a connection between this construction and families of
invariant Hermitian forms on the representations.