Finite Growth Representations of infinite Lie conformal algebra $gc_N.$

C. BOYALLIAN Y V. MEINARDI

Coimbra

Conferencia; Conference Non- Associative Algebras and Related Topics; 2011

In the present paper we classify all finite growth representations of all infinite rank conformal subalgebras of $gc_N$ that contain a Virasoro subalgebra. This problem reduces to the study of finite growth representations on the corresponding extended annihilation algebras, which are certain subalgebras of $\textit{D}^N$ . The main tools used here are the recent results on the classification of quasifinite highest weight modules over the central extension of $\textit{D}^N$ and some of its important subalgebras.