  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. These are closely related to the minimal grade
singular vectors in relaxed (parabolic) Verma modules. Further results include
an explicit presentation of Zhu's algebra and an elegant new proof of the
classification of simple relaxed highest weight modules over the corresponding
vertex operator algebra. These results suggest that generalisations to higher
rank fractional level models are now within reach.
