Temperley-Lieb-Jones category and the space of conformal blocks. (English) Zbl 1535.20181
Papadopoulos, Athanase (ed.), Essays in geometry. Dedicated to Norbert A’Campo. Berlin: European Mathematical Society. IRMA Lect. Math. Theor. Phys. 34, 813-846 (2023).
Summary: We describe a relationship between homological representations of the braid groups and the monodromy representations of the KZ connection. By using this topological method we show that there is an isomorphism between the space of conformal blocks and the space of morphisms of the Temperley-Lieb-Jones category, which is equivariant under the action of the braid group. We recover the unitarity of the braid group action on the space of conformal blocks by means of the positivity of the Markov trace.
For the entire collection see [Zbl 1519.57002].
For the entire collection see [Zbl 1519.57002].
MSC:
| 20F36 | Braid groups; Artin groups |
| 33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
