Speaker: Charles Young (University of Hertfordshire)
Abstract: The Wakimoto construction is an important tool in chiral conformal field theory and quantum integrable models. It provides a free-field realization for untwisted Kac-Moody algebras at arbitrary level. The core of this construction is a homomorphism of vertex algebras — due to Feigin and Frenkel in the case of g of arbitrary finite type — from the vacuum Verma module at the critical level, to a certain beta-gamma system.
I will review all this, and then ask: what happens if g itself is instead of affine type? That is, what happens in the case of double loop algebras and their extensions? It turns out that much of the construction goes through very naturally — in particular the required cocycle continues to exist — and the “critical level” turns out to be zero. What obstructions there are, are of a different nature, having to do with the treatment of certain infinite sums.
To state a theorem, I’ll deal with those infinite sums in a way which requires surrendering a free-field realization; but I’ll end by speculating that there should be a better way, involving some suitably generalized notion of vertex algebras.
This talk is based in part on “An analog of the Feigin-Frenkel homomorphism for double loop algebras” https://doi.org/10.1016/j.jalgebra.2021.07.031
Time: 14:00~16:00, Tuesday, Jan. 20, 2026.
Location: R1310, SIMIS
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