Abstract
We study the differential identities of the algebra UT2 of 2×2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L=Der(UT2) of derivations of UT2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group Sn and we determine the decomposition of the corresponding character into irreducibles.If V is the variety of differential algebras generated by UT2, we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth.
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