Classification of quasifinite representations of a Lie algebra related to Block type

Yucai Su, Chunguang Xia, Ying Xu

Published 2012-10-26Version 1

A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\BB$ related to Block type, with basis {L_{\a,i},C|a,i\in\Z, i\ge0} and relations [L_{\a,i},L_{\b,j}]=((i+1)\b-(j+1)\a)L_{\a+\b,i+j}+\d_{\a+\b,0}\d_{i+j,0}\frac{\a^3-\a}{6}C, [C,L_{\a,i}]=0.Namely, an irreducible quasifinite $\BB$-module is either a highest weight module, a lowest weight module or a module of the intermediate series.