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- W2952491202 abstract "The moduli space M(n,d) is an algebraic variety parametrizing those representations of the fundamental group of a punctured Riemann surface into the Lie group SU(n) for which a loop around the boundary is sent to the n-th root of unity exp (2 pi i d/n) multiplied by the identity matrix. If n and d are coprime it is in fact a Kahler manifold. One may relax the constraint and study moduli spaces M(L) parametrizing those representations for which the loop around the boundary is sent to an element conjugate to L, if L is some element in SU(n), and these are also Kahler manifolds for a suitable class of L. The Verlinde formula calculates the dimension of the space of holomorphic sections of certain line bundles over the spaces M(n,d) and M(L). We recall how a new proof of the Verlinde formula for M(n,d) given in joint work with Frances Kirwan may be obtained, and show how to modify this proof to obtain a proof of the variant of the Verlinde formula which applies to M(L) (the moduli space of parabolic bundles with one marked point) and to the analogous object with b marked points." @default.
- W2952491202 created "2019-06-27" @default.
- W2952491202 creator A5025851451 @default.
- W2952491202 date "2000-03-24" @default.
- W2952491202 modified "2023-09-27" @default.
- W2952491202 title "The Verlinde formula for parabolic bundles" @default.
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