  We explore the non-singlet sector of matrix quantum mechanics dual to $c=1$
Liouville theory. The non-singlets are obtained by adding $N_{f}\times N$
bi-fundamental fields in the gauged matrix quantum mechanics model as well as a
one dimensional Chern-Simons term. The present model is associated with a
spin-Calogero model in the presence of external magnetic field. In chiral
variables, the low energy excitations-currents satisfy an
${SU(2N_{f})}_{\tilde{k}}$ K\v{a}c-Moody algebra at large $N$. We analyse the
canonical partition function as well as two and four point correlation
functions, discuss a Gross-Witten-Wadia phase transition at large $N, N_f$ and
study different limits of the parameters that allow us to recover the matrix
model of Kazakov-Kostov-Kutasov conjectured to describe a two dimensional black
hole. The grand canonical partition function is a $\tau$- function obeying
discrete soliton equations. We finally conjecture a possible dynamical picture
for the formation of a black hole in terms of condensation of long-strings in
the strongly coupled region of the Liouville direction.
