A bosonization of U_q(sl(M|N))

par Takeo Kojima (Yamagata University, Japan)

vendredi 17 mars 2017, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Institut Camille Jordan)

Bosonization is a powerful method to study representation theory of infinite-dimensional algebras and its application to mathematical physics, such as calculation of correlation functions of exactly solvable models. For level k=1, bosonization has been constructed for the quantum affine algebra U_q(g) in many cases. Bosonization of an arbitrary level k in C is completely different from those of level k=1. For level k in C, bosonization has been constructed only for U_q(sl(N)) and U_q(sl(M|1)). In this talk we give a bosonization of the quantum affine superalgebra U_q(sl(M|N)) (M,N=1,2,3...) for an arbitrary level k. For the level k different from -M+N we give screening operators that commute with U_q(sl(M|N)) and propose a realization of the vertex operator. This talk is based on arXiv:1701.03645.