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We find new universal factorization identities for generalized Macdonaldpolynomials on the topological locus. We prove the identities (which includeall previously known forumlas of this kind) using factorization identities formatrix model averages, which are themselves consequences of Ding-Iohara-Mikiconstraints. Factorized expressions for generalized Macdonald polynomials areidentified with refined topological string amplitudes containing a toric braneon an intermediate preferred leg, surface operators in gauge theory and certaindegenerate CFT vertex operators.

Refined toric branes, surface operators and factorization of generalized Macdonald polynomials