Block型李代数B(q)的表示

Intrigued by a well-known theorem ofMathieu's on Harish-Chandra modules over the Virasoro algebra, weshow that any quasifinite irreducible module over a class of Blocktype Lie algebras B(q) is either a highest or lowest weight module, or elsea uniformly bounded module, where the parameter q is a nonzero complexnumber. We also classify quasifinite irreducible highest weightB(q)-modules and irreducible B(q)-modules of the intermediateseries. In particular, we obtain that an irreducible B(q)-module ofthe intermediate series may be a nontrivial extension of aVir-module of the intermediate series if q is half of anegative integer, where Vir is a subalgebra of B(q) isomorphicto the Virasoro algebra.