منابع مشابه
SLE martingales and the Virasoro algebra
We present an explicit relation between representations of the Virasoro algebra and polynomial martingales in stochastic Loewner evolutions (SLE). We show that the Virasoro algebra is the spectrum generating algebra of SLE martingales. This is based on a new representation of the Virasoro algebra, inspired by the Borel-Weil construction, acting on functions depending on coordinates parametrizin...
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X iv :0 80 1. 22 09 v1 [ m at h. R A ] 1 5 Ja n 20 08 Representations of the Schrödinger-Virasoro algebras Junbo Li, Yucai Su ∗)Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China †)Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China ‡)Department of Mathematics, University of Science and Technology of China, Hefei 230026, China E-mail...
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We show how to relate Schramm-Loewner Evolutions (SLE) to highestweight representations of infinite-dimensional Lie algebras that are singular at level two, using the conformal restriction properties studied by Lawler, Schramm and Werner in [33]. This confirms the prediction from conformal field theory that two-dimensional critical systems are related to degenerate representations.
متن کاملOn unitary representations of the Virasoro algebra
Some representations π of b of particular interest [2] are the Verma modules (V, π) = (V , π), h, c ǫ R. They are characterized by the following conditions. (i) There is a vector v = vφ 6= 0 in V such that Lnv = 0, n > 0, L0v = hv, Zv = cv. (ii) Let A be the set of sequences of integers k1,≥ k2 ≥ . . . ≥ kr > 0 of arbitrary length, and if α ǫ A let vα = π(L−k1) . . . π(L−kr)vφ. Then {vα|α ǫ A} ...
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We consider representations of the Virasoro algebra, a one-dimensional central extension of the Lie algebra of vectorfields on the unit circle. Positive-energy, highest weight and Verma representations are defined and investigated. The Shapovalov form is introduced, and we study Kac formula for its determinant and some consequences for unitarity and degeneracy of irreducible highest weight repr...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2015
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-014-2283-7