  We show that the XY quantum chain in a magnetic field is invariant under a
two parameter deformation of the $SU(1/1)$ superalgebra. One is led to an
extension of the braid group and the Hecke algebras which reduce to the known
ones when the two parameter coincide. The physical significance of the two
parameters is discussed. When both are equal to one, one gets a
Pokrovski-Talapov phase transition. We also show that the representation theory
of the quantum superalgebras indicates how to take the appropriate
thermodynamical limits.
