Let $\mathfrak{g}$ be a finite dimensional simple Lie algebra, and $M(\Lambda)$ the Verma module with dominant integral highest weight $\Lambda$. The singular vectors in $M(\Lambda)$ are well known (they are something like $f_i^{\Lambda(h_i^\vee)+1} v_\Lambda$). A similar fact is true for the affine Lie algebra $\widehat{\mathfrak{g}}$, with integrable highest weight.

I know of a paper by Feigin, Fuchs and Malikov (1986) where an explicit formula for singular vectors is given for Verma modules over $\widehat{\mathfrak{sl}_2}$ with more general highest weight. The answer uses a notation involving Lie algebra elements raised to complex powers!

My question is about how much is known for more general Lie algebras, and where can I find information.

For instance, have formulas for singular vectors in $M(\Lambda)$ been given for every highest weight $\Lambda$ over any affine Lie algebra $\widehat{\mathfrak{g}}$? Or has little been done since Feigin, Fuchs and Malikov.

Also, I wonder if the answer to my question exists already but in some different (perhaps more abstract) language?

Thanks, Jethro