Free field realization of the Ding-Iohara algebra at general levels

Abstract

We present a unified free field realization of the Ding-Iohara algebra at arbitrary levels, which satisfies a generalized form of the Serre relations. This realization, constructed using six free boson fields, arises from a specialized factorization of the structure function in the defining relations of the algebra. Based on this construction, we then develop intertwining operators for the Ding-Iohara algebra.

49 pages, no figure. v3: major revisions with respect to the Serre relations; a generalized form of the Serre relations proposed in Section 3.4; detailed calculations added in the appendix; some typos corrected

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