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.
Categories: math.RT