Sets of rigged paths with Virasoro characters |
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| Authors: | B Feigin M Jimbo T Miwa E Mukhin Y Takeyama |
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| 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 |
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| Abstract: | Let {M
r,s
(p,p′)}1≤r≤p−1,1≤s≤p′−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
, 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
. 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.
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| Keywords: | Virasoro algebra Minimal series Primary fields Monomial basis |
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