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A φ1,3-Filtration of the Virasoro Minimal Series M(p, p') with 1 < p'/p < 2Boris Feigin, Evgeny Feigin, M. Jimbo, Tetsuji Miwa and Y. Takeyama (1) Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002, Moscow, Russian Federation
(2) Department of Mathematics, National Research University Higher School of Economics, Vavilova St 7, 117312, Moscow, Russian Federation
(3) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, 153-8914, Tokyo, Japan
(4) Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan
(5) Institute of Mathematics, Graduate School of Pure and Applied Sciences, University of Tsukuba, 305-8571, Ibaraki, Japan
The ﬁltration of the Virasoro minimal series representations Mr,s(p, p') induced by the (1, 3)-primary ﬁeld φ1,3(z) 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 coeffcients 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).
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Feigin Boris, Feigin Evgeny, Jimbo M., Miwa Tetsuji, Takeyama Y.: A φ1,3-Filtration of the Virasoro Minimal Series M(p, p') with 1 < p'/p < 2. Publ. Res. Inst. Math. Sci. 44 (2008), 213-257. doi: 10.2977/prims/1210167327