The filtration of the Virasoro minimal series representations M r,s(p,p′) induced by the (1,3)-primary field φ1,3(3) is studied. For 1 < p′/p < 2, a conjectural basis of Mr,s(p,p′) compatible with the filtration is given by using monomial vectors in terms of the Fourier coefficients of φ1,3(z). In support of this conjecture, we give two results. First, we establish the equality of the character of the conjectural basis vectors with the character of the whole representation space. Second, for the unitary series (p′ = p + 1), we establish for each m the equality between the character of the degree m monomial basis and the character of the degree m component in the associated graded module gr(Mr,s(p,p+1))) with respect to the filtration defined by φ1,3(z).
|Number of pages||45|
|Journal||Publications of the Research Institute for Mathematical Sciences|
|State||Published - May 2008|