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Vertex algebras and algebraic curves
 Mathematical Surveys and Monographs 88 (2001), Amer. Math.Soc. MR1849359 (2003f:17036
"... Vertex operators appeared in the early days of string theory as local operators describing propagation of string states. Mathematical analogues of these operators were discovered in representation theory of affine KacMoody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK]. In or ..."
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Cited by 177 (10 self)
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Vertex operators appeared in the early days of string theory as local operators describing propagation of string states. Mathematical analogues of these operators were discovered in representation theory of affine KacMoody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK]. In order to formalize the emerging structure and motivated
The line bundles on the moduli of parabolic Gbundles over curves and their sections
, 1996
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Vertex Operator Algebras, the Verlinde Conjecture and Modular Tensor Categories
, 2005
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Infinite Grassmannians and moduli spaces of Gbundles
 Math. Annalen
, 1994
"... These are notes for my eight lectures given at the C.I.M.E. session on “Vector bundles on curves. New directions ” held at Cetraro (Italy) in June 1995. The work presented here was done in collaboration with M.S. Narasimhan and A. Ramanathan and appeared in [KNR]. These notes differ from [KNR] in th ..."
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Cited by 68 (4 self)
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These are notes for my eight lectures given at the C.I.M.E. session on “Vector bundles on curves. New directions ” held at Cetraro (Italy) in June 1995. The work presented here was done in collaboration with M.S. Narasimhan and A. Ramanathan and appeared in [KNR]. These notes differ from [KNR] in that we have
Twisted equivariant Ktheory with complex coefficients
, 2008
"... Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space ..."
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Cited by 67 (5 self)
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Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space
Conformal blocks, fusion rules and the Verlinde formula
 BarIlan Univ
, 1993
"... The Verlinde formula computes the dimension of certain vector spaces, the spaces of conformal blocks, which are the basic objects of a particular kind of quantum field theories, the socalled Rational Conformal Field Theories (RCFT). These spaces appear as spaces of global multiform sections of some ..."
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Cited by 67 (0 self)
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The Verlinde formula computes the dimension of certain vector spaces, the spaces of conformal blocks, which are the basic objects of a particular kind of quantum field theories, the socalled Rational Conformal Field Theories (RCFT). These spaces appear as spaces of global multiform sections of some flat vector
Vector bundles on curves and generalized theta functions: recent results and open problems
 CAMBRIDGE UNIVERSITY PRESS
, 1995
"... The moduli spaces of vector bundles on a compact Riemann surface carry a natural line bundle, the determinant bundle. The sections of this line bundle and its multiples constitute a nonabelian generalization of the classical theta functions. New ideas coming from mathematical physics have shed a ..."
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Cited by 58 (3 self)
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The moduli spaces of vector bundles on a compact Riemann surface carry a natural line bundle, the determinant bundle. The sections of this line bundle and its multiples constitute a nonabelian generalization of the classical theta functions. New ideas coming from mathematical physics have shed a new light on these spaces of sections—allowing notably to compute their dimension (Verlinde’s formula). This survey paper is devoted to giving an overview of these ideas and of the most important recent results on the subject.
Principal Gbundles over elliptic curves
, 1998
"... 1. Introduction. Let E be an elliptic curve with origin p0, and let G be a complex simple algebraic group. For simplicity, we shall only consider the case where G is simply connected, although all of the methods discussed below can be extended to the case of a general group G. The goal of this note ..."
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Cited by 49 (3 self)
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1. Introduction. Let E be an elliptic curve with origin p0, and let G be a complex simple algebraic group. For simplicity, we shall only consider the case where G is simply connected, although all of the methods discussed below can be extended to the case of a general group G. The goal of this note is to announce some results concerning the
Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups in the singular case
 In preparation
"... Abstract. We prove that the sequence of projective quantum SU(n) representations of the mapping class group of a closed oriented surface, obtained from the projective flat SU(n)Verlinde bundles over Teichmüller space, is asymptotically faithful, that is the intersection over all levels of the kerne ..."
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Abstract. We prove that the sequence of projective quantum SU(n) representations of the mapping class group of a closed oriented surface, obtained from the projective flat SU(n)Verlinde bundles over Teichmüller space, is asymptotically faithful, that is the intersection over all levels of the kernels of these representations is trivial, whenever the genus is at least 3. For the genus 2 case, this intersection is exactly the order two subgroup, generated by the hyperelliptic involution, in the case of even degree and n = 2. Otherwise the intersection is also trivial in the genus 2 case. 1.