The special linear group G=SL_n(Z[x1,...,xk]) (n at least 3 and k finite) iscalled the universal lattice. Let n be at least 4, p be any real number in(1,infty). The main result is the following: any finite index subgroup of Ghas the fixed point property with respect to every affine isometric action onthe space of p-Schatten class operators. It is in addition shown that higherrank lattices have the same property. These results are generalization ofprevious theorems repsectively of the author and ofBader--Furman--Gelander--Monod, which treated commutative Lp-setting.
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