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Conformal blocks, Verlinde formula and diagram automorphisms

Research paper by Jiuzu Hong

Indexed on: 10 Oct '16Published on: 10 Oct '16Published in: arXiv - Mathematics - Representation Theory



Abstract

The Verlinde formula computes the dimension of conformal blocks associated to simple Lie algebras and stable pointed curves. If a simple Lie algebra admits a nontrivial diagram automorphism, then this automorphism acts on the space of conformal blocks naturally. We prove an analogue of Verlinde formula for the trace of the diagram automorphism on conformal blocks. A non simply-laced Lie algebra appears in the formula. Motivated by this formula and Jantzen's twining formula, we make a conjecture on the Verlinde formula for the dimension of conformal blocks associated to twisted affine Lie algebras.