Abstract: 
A HermanAvilaBochi type formula is obtained for the average sum of the top d Lyapunov exponents over a oneparameter family of doublestruck Gcocycles, where doublestruck G is the group that leaves a certain, nondegenerate Hermitian form of signature (c, d) invariant. The generic example of such a group is the pseudounitary group U(c, d) or, in the case c = d, the Hermitiansymplectic group HSp(2d) which naturally appears for cocycles related to Schrödinger operators. In the case d = 1, the formula for HSp(2d) cocycles reduces to the HermanAvilaBochi formula for SL(2, ℝ) cocycles.
