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187
Two dimensional gauge theories revisited
 J. Geom. Phys
, 1992
"... Two dimensional quantum YangMills theory is reexamined using a nonabelian version of the DuistermaatHeckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressi ..."
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Cited by 200 (3 self)
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Two dimensional quantum YangMills theory is reexamined using a nonabelian version of the DuistermaatHeckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional surface. The latter expressions agree, for gauge group SU(2), with formulas obtained recently by several methods. This paper will be devoted to a renewed study of two dimensional YangMills theory without matter, a system which can be easily solved [1] and has been extensively studied [2–10]. Yet we will see that there is still much to say about this supposedly “trivial ” system. To state our result in a nutshell, we will explain (in
Conformal blocks and generalized theta functions
 Comm. Math. Phys
, 1994
"... The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as foll ..."
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Cited by 141 (8 self)
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The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as follows: choose a point p ∈ X, and let AX be the
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 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
Tensor products of modules for a vertex operator algebras and vertex tensor categories
 in: Lie Theory and Geometry, in honor of Bertram Kostant
, 1994
"... In this paper, we present a theory of tensor products of classes of modules for a vertex operator algebra. We focus on motivating and explaining new structures and results in this theory, rather than on proofs, which are being presented in a series of papers beginning with [HL4] and [HL5]. An announ ..."
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Cited by 68 (13 self)
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In this paper, we present a theory of tensor products of classes of modules for a vertex operator algebra. We focus on motivating and explaining new structures and results in this theory, rather than on proofs, which are being presented in a series of papers beginning with [HL4] and [HL5]. An announcement has also appeared [HL1].
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.