  We prove analogues for elliptic interpolation functions of Macdonald's
version of the Littlewood identity for (skew) Macdonald polynomials, in the
process developing an interpretation of general elliptic "hypergeometric" sums
as skew interpolation functions. One such analogue has an interpretation as a
"vanishing integral", generalizing a result of arXiv:math/0606204; the
structure of this analogue gives sufficient insight to enable us to conjecture
elliptic versions of most of the other vanishing integrals of
arXiv:math/0606204 as well. We are thus led to formulate ten conjectures, each
of which can be viewed as a multivariate quadratic transformation, and can be
proved in a number of special cases.
