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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
The Nil Hecke Ring And Singularity Of Schubert Varieties
, 1995
"... this paper. We use this theorem to prove that b w \Gamma1 6= 0 if and only if v w, and in this case it has a pole of order exactly equal to `(w). Similarly \Gamma1 6= 0 if and only if v w (cf. Corollaries 3.2) ..."
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Cited by 39 (0 self)
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this paper. We use this theorem to prove that b w \Gamma1 6= 0 if and only if v w, and in this case it has a pole of order exactly equal to `(w). Similarly \Gamma1 6= 0 if and only if v w (cf. Corollaries 3.2)
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 38 (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
Birational Weyl group action arising from a nilpotent Poisson algebra
 in Proc. of the Nagoya 1999 International Workshop “Physics and Combinatorics 1999” (Nagoya), World Sci. Publ., River Edge, NJ
"... We propose a general method to realize an arbitrary Weyl group of KacMoody type as a group of birational canonical transformations, by means of a nilpotent Poisson algebra. ..."
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We propose a general method to realize an arbitrary Weyl group of KacMoody type as a group of birational canonical transformations, by means of a nilpotent Poisson algebra.
Cohomology of line bundles on Schubert varieties in the KacMoody setting
, 2006
"... In this paper, we describe the indices of the top and the least nonvanihing cohomologies H i (X(w),Lλ) of line budles on Schubert varieties X(w) given by nondominant weights in the KacMoody setting. We also prove some surjective Theorem for maps between some cohomology modules. 1 ..."
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Cited by 7 (3 self)
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In this paper, we describe the indices of the top and the least nonvanihing cohomologies H i (X(w),Lλ) of line budles on Schubert varieties X(w) given by nondominant weights in the KacMoody setting. We also prove some surjective Theorem for maps between some cohomology modules. 1