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Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

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This book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.

Author(s): Shrawan Kumar
Series: New Mathematical Monographs 42
Publisher: Cambridge University Press
Year: 2021

Language: English
Pages: XXVIII+510

Contents
Preface
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
Appendix A - Dynkin Index
Appendix B - C-Space and C-Group Functors
Appendix C - Algebraic Stacks
Appendix D - Rank-Level Duality (A Brief Survey)
Bibliography
Index