Irreducible modules over finite simple conformal superálgebras of type W, S and K

LIBERATI, JOSE I.

Workshop; International Workshop & Conference on Infinite Dimensional Lie Theory and its Applications; 2011

A complete classification of finite simple Lie conformal superalgebraswas obtained in[FK]. The list consists of current Lie conformal superalgebras Cur g,where g is a simplefinite-dimensional Lie superalgebra, the series of “Virasoro-like” Lieconformal superalgebrasof type W, S and K, the derived algebra K4' and the exceptional Lieconformal superalgebraCK6. In this talk, we present the classification and construction ofall finite irreducible modules over Lie conformal superalgebras oftype W, S and K (joint work with C. Boyallian and V. Kac [BKLR-BKL]). [FK] Fattori, D. and Kac, V. G., "Classification of finite simple Lieconformal superalgebras", J. Algebra 258 (2002).[BKLR] Boyallian, C., Kac, V. G., Liberati, J., and Rudakov, A.,"Representations of simple finite Lie conformal superalgebrasof type W and S", J. Math. Phys. 47, (2006).[BKL] Boyallian, C., Kac, V. G., Liberati, J., "Irreducible modulesover  finite simple Lie conformal superalgebras of type K", J. Math.Phys. 51, (2010).