  This note continues paper of Denisov and Wachtel (2010), where we have
constructed a $k$-dimensional random walk conditioned to stay in the Weyl
chamber of type $A$. The construction was done under the assumption that the
original random walk has $k-1$ moments. In this note we continue the study of
killed random walks in the Weyl chamber, and assume that the tail of increments
is regularly varying of index $\alpha<k-1$. It appears that the asymptotic
behaviour of random walks is different in this case. We determine the
asymptotic behaviour of the exit time, and, using thisinformation, construct a
conditioned process which lives on a partial compactification of the Weyl
chamber.
