Conformal Blocks, Generalized Theta Functions and the Verlinde Formula - Kumar, Shrawan

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Résumé :
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Biographie:
Shrawan Kumar is John R. and Louise S. Parker Distinguished Professor of Mathematics at the University of North Carolina, Chapel Hill. He was an invited Speaker at the 2010 International Congress of Mathematicians and was elected a Fellow of the American Mathematical Society in 2012. This is his third book.

Sommaire:
Introduction; 1. An introduction to affine Lie algebras and the associated groups; 2. Space of vacua and its propagation; 3. Factorization theorem for space of vacua; 4. Fusion ring and explicit Verlinde formula; 5. Moduli stack of quasi-parabolic G-bundles and its uniformization; 6. Parabolic G-bundles and equivariant G-bundles; 7. Moduli space of semistable G-bundles over a smooth curve; 8. Identification of the space of conformal blocks with the space of generalized theta functions; 9. Picard group of moduli space of G-bundles; A. Dynkin index; B. C-space and C-group functors; C. Algebraic stacks; D. Rank-level duality (A brief survey) Swarnava Mukhopadhyay; Glossary; Bibliography; Index.