Séminaire de Physique Théorique

A bosonization of the superalgebra $U_q(\widehat{sl}(M|N))$ for level $k \in {\bf C}$
Takeo Kojima (Department of Mathematics and Physics, Yamagata University)
Thursday 08 September 2016 14:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
We give a bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ for level $k \in {\bf C}$. We give a bosonization of the screening operator that commutes with $U_q(\widehat{sl}(M|N))$ for level $k \neq N-M$.Using the screening operator we propose a bosonization of the vertex operator. This talk gives a generalization of [1, 2, 3]. References: [1]T.Kojima, Free field realization of quantum affine superalgebra $U_q(\widehat{sl}(N|1))$, {\it J.Math.Phys.} {\bf 53}, 013515 (2012). [2]T.Kojima, Screenings and vertex operators of quantum superalgebra $U_q(\widehat{sl}(N|1))$, {\it J.Math.Phys.} {\bf 53}, 083503 (2012). [3]B.Feigin and E.Frenkel, Representation of affine Kac-Moody algebras and bosonization, {\it Physics and Mathematics of Strings} (World Scientific, Singapore, 1990), pp.271-316.

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