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A bijection between paths for the M(p,2p+1) minimal model Virasoro characters

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 Added by Pierre Mathieu
 Publication date 2009
  fields Physics
and research's language is English




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The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the M(p,2p+1) models, a completely different path representation has been found recently, this one on a half-integer lattice; it has no known underlying statistical-model interpretation. The correctness of this alternative representation has not yet been demonstrated, even at the level of the generating functions, since the resulting fermionic characters differ from the known ones. This gap is filled here, with the presentation of t



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56 - B. Feigin , E. Feigin , M. Jimbo 2006
The filtration of the Virasoro minimal series representations M^{(p,p)}_{r,s} induced by the (1,3)-primary field $phi_{1,3}(z)$ is studied. For 1< p/p< 2, a conjectural basis of M^{(p,p)}_{r,s} compatible with the filtration is given by using monomial vectors in terms of the Fourier coefficients of $phi_{1,3}(z)$. 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^{(p,p+1)}_{r,s}) with respect to the filtration defined by $phi_{1,3}(z)$.
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