QHWM of the Lie subalgebras of the Lie algebra WN 1+1

C. BOYALLIAN Y V. MEINARDI

Mendoza

Encuentro; Colloquium on Hopf algebras, Quantum Groups and Tensor Categories; 2011

We classify the irreducible quasinite highest weight modules of the orthogonal Lie subalgebra and the Lie subalgebra WN 1;p; of WN 1+1 which denotes the Lie algebra of matrix dierential operators on the circle. We also realize them in terms of the representations theory of the complex Lie algebra g`[m] 1 of innite matrices with a nite number of non-zero diagonals with entries in the algebra of truncated polynomials, and the corresponding subalgebras of type B, C and D. The aim is to give a general theorem for for quasinitness of irreducible highest weight modules of Lie subalgebras of WN 1+1: Re