Supersymmetric Racah Basis, Family of Infinite-Dimensional Superalgebras, SU(∞+1|∞) and Related 2d Models

The irreducible Racah basis for SU(N+1|N) is introduced. An analytic continuation with respect to N leads to infinite-dimensional superalgebras su(v+1|v). The large-v limit su(∞+1|∞) is calculated. A higher spin Sugawara construction leading to generalizations of the Virasoro algebra with infinite tower of higher spin currents is proposed, and the related WZNW and Toda models as well as the possible applications in string theory are discussed.