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Sets of rigged paths with Virasoro characters
Authors:B Feigin  M Jimbo  T Miwa  E Mukhin  Y Takeyama
Institution:(1) Landau Institute for Theoretical Physics, Chernogolovka, 142432, Russia;(2) Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan;(3) Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan;(4) Department of Mathematics, Indiana University-Purdue University-Indianapolis, 402 N. Blackford St., LD 270, Indianapolis, IN 46202, USA;(5) Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Abstract:Let {M r,s (p,p′)}1≤rp−1,1≤sp′−1 be the irreducible Virasoro modules in the (p,p′)-minimal series. In our previous paper, we have constructed a monomial basis of r=1 p−1 M r,s (p,p′) in the case 1<p′/p<2. By ‘monomials’ we mean vectors of the form $\phi^{(r_{L},r_{L-1})}_{-n_{L}}\cdots\phi^{(r_{1},r_{0})}_{-n_{1}}{|r_{0},s\rangle }$ , where φ n (r′,r):M r,s (p,p′)M r′,s (p,p′) are the Fourier components of the (2,1)-primary field and |r 0,s〉 is the highest weight vector of $M^{(p,p')}_{r_{0},s}$ . In this article, we introduce for all p<p′ with p≥3 and s=1 a subset of such monomials as a conjectural basis of r=1 p−1 M r,1(p,p′). We prove that the character of the combinatorial set labeling these monomials coincides with the character of the corresponding Virasoro module. We also verify the conjecture in the case p=3.
Keywords:Virasoro algebra  Minimal series  Primary fields  Monomial basis
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