We study various specializations of the colored HOMFLY-PT polynomial. These
specializations are used to show that the multivariable link invariants arising
from a complex family of sl(m|n) super-modules previously defined by the
authors contains both the multivariable Alexander polynomial and Kashaev's
invariants. We conjecture these multivariable link invariants also specialize
to the generalized multivariable Alexander invariants defined by Y. Akutsu, T.
Deguchi, and T. Ohtsuki.Comment: 16 page