Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models

Understand

The fractional level models are (logarithmic) conformal field theories associated with affine Kac-Moody (super)algebras at certain levels $k \in \mathbb{Q}$.

• They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved.
• Here, Wakimoto's free field realisation is combined with the theory of Jack symmetric functions to analyse the fractional level $\widehat{\mathfrak{sl}}(2)$ models.
• The first main results are explicit formulae for the singular vectors of minimal grade in relaxed Wakimoto modules.