Modular functor and representation theory of ̂𝑠𝑙₂ at a rational level

Abstract

We define a new modular functor based on Kac-Wakimoto admissible representations and the corresponding D−module on the moduli space of rank 2 vector bundles with the parabolic structure. A new fusion functor arises which is related to representation theory of the pair "osp(1|2), sl 2 " in the same way as the fusion functor for the Virasoro algebra is related to representation theory of the pair "sl 2 , sl 2 ".

An Algebraic Approach to Logarithmic Conformal Field Theory

“…Two different sets of 'fusion rules' have been proposed in the literature: the fusion rules of Bernard and Felder [68] whose calculations have been reproduced in [71,74], and the fusion rules of Awata and Yamada [70] whose results have been recovered in [72,73,75,76,77] [72,78].) This modified notion of fusion is physically not very well motivated, and it falls outside the usual framework of vertex operator algebras; in the following we shall therefore consider the usual definition of fusion.…”

Joseph Ideals and Lisse Minimal -Algebras

“…It would be very interesting to consider the associated modular functor (cf. [FM97]), or the corresponding conformal field theory (cf. [CR12,CR13]).…”

Fusion in coset CFT from admissible singular-vector decoupling

“…We restricted to this coset for simplicity, and because decoupling fusion has only been worked out completely in the su(2) case. 9 We should emphasise again that WZW models at fractional levels may not be consistent, except in coset theories. After all, the Verlinde fusion coefficients are sometimes negative integers.…”

“…We also found direct descriptions for such truncations. Particular attention was paid to a 9 Complete results for certain levels are now known for su(3) [19]. truncation motivated by the notion of highest and lowest weights in the derivation of the singular-vector decoupling fusions.…”