2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153639We review the W_N algebra and its quantum deformation, based on free field realizations. The (quantum deformed) W_N algebra is defined through the (quantum deformed) Miura transformation, and its singular vectors realize the Jack (Macdonald) polynomials. (Talk at the Nankai-CRM joint meeting on ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin, China, August 19-24, 1996.)18 pages, LaTeXQuantum AlgebraHigh Energy Physics - Theorytext