Factorizations of 3d Interval Partition Functions

We show that interval partition functions (transition amplitudes) of three-dimensional $N=2$ theories admit factorizations into sums of products of hemisphere partition functions with additional normalization factors. We prove the factorization explicitly for supersymmetric quantum electrodynamics and Chern-Simons-Yang-Mills theories. In the former case, we interpret the factorization geometrically in terms of the factorization of equivariant K-theory classes. In the latter case, we prove that hemisphere partition functions are affine characters and determine the normalization factors explicitly in special cases.