  We find new universal factorization identities for generalized Macdonald
polynomials on the topological locus. We prove the identities (which include
all previously known forumlas of this kind) using factorization identities for
matrix model averages, which are themselves consequences of Ding-Iohara-Miki
constraints. Factorized expressions for generalized Macdonald polynomials are
identified with refined topological string amplitudes containing a toric brane
on an intermediate preferred leg, surface operators in gauge theory and certain
degenerate CFT vertex operators.
