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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 176 (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 72 (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 71 (8 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 69 (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 61 (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.
Vilonen Perverse Sheaves on affine Grassmannians and Langlands Duality, electronic preprint math.AG/9911050
"... In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group L G is naturally equivalent to ..."
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Cited by 56 (3 self)
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In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group L G is naturally equivalent to
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 51 (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
Appendix to Twisted Loop Groups and their affine flag varieties by
 Advances in Math. 219
, 2008
"... Loop groups are familiar objects in several branches of mathematics. Let us mention here three variants. The first variant is differentialgeometric in nature. One starts with a Lie group G (e.g., a compact Lie group or its complexification). The associated loop group is then the group ..."
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Cited by 48 (4 self)
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Loop groups are familiar objects in several branches of mathematics. Let us mention here three variants. The first variant is differentialgeometric in nature. One starts with a Lie group G (e.g., a compact Lie group or its complexification). The associated loop group is then the group