Free field realization of q-deformed primary fields for U_q(\widehat\sl₂)

1992/12/05 by Akira Matsuo, Matsuo, A. · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.hep-th/9212040

openalex publication_date 1992/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The q-vertex operators of Frenkel and Reshetikhin are studied by means of a q-deformation of the Wakimoto module for the quantum affine algebra U_q(\widehat\sl₂) at an arbitrary level k≠ 0,-2. A Fock module version of the q-deformed primary field of spin j is introduced, as well as the screening operators which (anti-)commute with the action of U_q(\widehat\sl₂) up to a total difference of a field. A proof of the intertwining property is given for the q-vertex operators corresponding to the primary fields of spin j∉ 1 \over2\Z_≥0, which is enough to treat a general case. A sample calculation of the correlation function is also given.

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• Representations at a Root of Unity of q-Oscillators and Quantum Kac-Moody algebras

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