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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 93 (9 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
"... ..."
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 49 (2 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 46 (6 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
Vector bundles on curves and generalized theta functions: recent results and open problems
 Cambridge University Press
, 1995
"... Abstract. 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 ..."
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Cited by 43 (2 self)
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Abstract. 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 42 (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 37 (2 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
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 35 (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
Hitchin's and WZW connections are the same
, 1998
"... Introduction :\Gamma Let X be an algebraic curve over the field C of complex numbers which is assumed to be smooth, connected and projective. For simplicity, we assume that the genus of X is ? 2 . Let G be a simple simply connected group and MG (X) the coarse moduli scheme of semistable Gbundles on ..."
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Cited by 23 (2 self)
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Introduction :\Gamma Let X be an algebraic curve over the field C of complex numbers which is assumed to be smooth, connected and projective. For simplicity, we assume that the genus of X is ? 2 . Let G be a simple simply connected group and MG (X) the coarse moduli scheme of semistable Gbundles on X . Any linear representation determines a line bundle \Theta on M and some non negative integer l (the Dynkin index of the representation, cf [KNR], [LS]). Its is known that the choice of a (closed) point x 2 X(C) (and, a priori, of a formal coordinate near x ) of X determines an isomorphism (see (5.4)) between the projective space of conformal blocks PB l (X) (for G ) of level l and the space PH 0 (MG (X); \Theta) of generalized theta