Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis

We study a vertex operator algebra (VOA)Vrelated to the M(3, p) Virasoro minimal series. This VOA reduces in the simplest case p = 4 to the level-two integrable vacuum module of \({\widehat {sl}_2}\). On V there is an action of a commutative current a(z), which is an analog of the current e(z) of \({\widehat {sl}_2}\). Our main concern is the subspace W generated by this action from the highest weight vector of V. Using the Fourier components of a(z), we present a monomial basis of W and a semi-infinite monomial basis of V. We also give a Gordon type formula for their characters.