Abstract:

The twisted Kac-Moody Lie superalgebra $\widehat{psl(2|2)^{(2)}}_k$
is investigated by means of the vector coherent state method and
obtained the differential operators realization.
The authors get the free field representation of
$\widehat{psl(2|2)^{(2)}}_k$, which is the subalgebra of
$\widehat{gl(2|2)^{(2)}}_k$ modulo the ${\Bbb Z}_4$-outer
automorphism, the CFT has central charge $-2.$\noindent{\bf Key words:}Kac-Moody superalgebra; Differential operator realization; Free field realization; Conformal field theory.

Key words: Kac-Moody superalgebra, Differential operator realization, Free field realization, Conformal field theory