Invariants of quasitrivial tori and the Rost invariant

For any absolutely simple, simply connected linear algebraic group $G$ over a field $F$. Rost has defined invariants for the torsors under $G$ with values in the Galois cohomology group $H^3(F,\mathbb Q/\mathbb Z(2))$. In this paper, an explicit description of these invariants is given for the torsors induced from the center of $G$ in the case where $G$ is of type $A_n$ or $D_n$. As an application, it is shown that the multipliers of the unitary similitudes satisfy a relation involving the discriminant algebra.