TY - JOUR
T1 - A φ1,3-filtration of the virasoro minimal series M(p,p′) with 1 < p′/p < 2
AU - Feigin, B.
AU - Feigin, E.
AU - Jimbo, M.
AU - Miwa, T.
AU - Takeyama, Y.
PY - 2008/5
Y1 - 2008/5
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=47749126575&partnerID=8YFLogxK
U2 - 10.2977/prims/1210167327
DO - 10.2977/prims/1210167327
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AN - SCOPUS:47749126575
SN - 0034-5318
VL - 44
SP - 213
EP - 257
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
IS - 2
ER -