Geometrization of the TUY/WZW/KZ connection

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Vector bundles on curves and their moduli (14H60) Geometric quantization (53D50) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

Cites Work

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Nonvanishing of conformal blocks divisors on \(\overline{\mathrm{M}}_{0,n} \)
Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization
Poincaré families of \(G\)-bundles on a curve
Non-Abelian bosonization in two dimensions
Strange duality and the Hitchin/WZW connection
Geometric quantization of Chern-Simons gauge theory
Uniformization of \({\mathcal {G}}\)-bundles
Monodromy representations of braid groups and Yang-Baxter equations
Demazure character formula in arbitrary Kac-Moody setting
Infinite conformal symmetry in two-dimensional quantum field theory
Modular and conformal invariance constraints in representation theory of affine algebras
Current algebras and Wess-Zumino model in two dimensions
Determinant bundles and Virasoro algebras
Moduli of vector bundles on curves with parabolic structures
Arrangements of hyperplanes and Lie algebra homology
The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem
Determinants of parabolic bundles on Riemann surfaces
On the coordinate-free description of the conformal blocks
Moduli of parabolic G-bundles on curves
Faltings' construction of the K-Z connection
On algebraic equations satisfied by hypergeometric correlators in WZW models. I
Conformal blocks and generalized theta functions
Infinite Grassmannians and moduli spaces of \(G\)-bundles
Picard group of the moduli spaces of \(G\)-bundles
Parabolic bundles as orbifold bundles
Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants.
Stable principal bundles on a compact Riemann surface
On algebraic equations satisfied by hypergeometric correlators in WZW models. II
Lie algebra cohomology and the fusion rules
\(B\)-structures on \(G\)-bundles and local triviality
Moduli spaces of parabolic fibres and conformal blocks
Generalized theta functions, strange duality, and odd orthogonal bundles on curves
Halbeinfache Gruppenschemata über Dedekindringen
Stable and unitary vector bundles on a compact Riemann surface
Flat connections and geometric quantization
Chern classes of conformal blocks
Moduli of parahoric 𝒢-torsors on a compact Riemann surface
Moduli of parabolic Higgs bundles and Atiyah algebroids
Vanishing and identities of conformal blocks divisors
The Hamiltonian formalism and a many-valued analogue of Morse theory
On moduli of G-bundles on a curve for exceptional G
The line bundles on the moduli of parabolic G-bundles over curves and their sections
On Hitchin’s connection
On Moduli of G-bundles over Curves for exceptional G
Triviality Properties of Principal Bundles on Singular Curves. II
Triviality properties of principal bundles on singular curves
Complete Integrability of the Parahoric Hitchin System
JACOBI COHOMOLOGY, LOCAL GEOMETRY OF MODULI SPACES, AND HITCHIN CONNECTIONS
MODULI SPACES OF PARABOLIC HIGGS BUNDLES AND PARABOLIC K(D) PAIRS OVER SMOOTH CURVES: I
THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC
Hitchin's connection and differential operators with values in the determinant bundle
Hitchin's and WZW connections are the same
A Hitchin connection on nonabelian theta functions for parabolic \(G\)-bundles
Crossed modular categories and the Verlinde formula for twisted conformal blocks