## Abstract

The filtration of the Virasoro minimal series representations M _{r,s}^{(p,p′)} induced by the (1,3)-primary field φ_{1,3}(3) is studied. For 1 < p′/p < 2, a conjectural basis of M_{r,s}^{(p,p′)} compatible with the filtration is given by using monomial vectors in terms of the Fourier coefficients of φ_{1,3}(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(M_{r,s}^{(p,p+1)})) with respect to the filtration defined by φ_{1,3}(z).

Original language | English |
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Pages (from-to) | 213-257 |

Number of pages | 45 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 44 |

Issue number | 2 |

DOIs | |

State | Published - May 2008 |

Externally published | Yes |

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