The [Weyl character formula](https://en.wikipedia.org/wiki/Weyl_character_formula) and [the denominator identity](https://en.wikipedia.org/wiki/Weyl_character_formula#Weyl_denominator_formula) play important roles in the representation theory of classical simple Lie algebras and Kac-Moody Lie algebras over $\mathbb{C}$


Can you suggest any reference for similar formulas for Lie super-algebras? I suppose there are such formulas, at least for classes of (say classical simple) Lie super-algebras.



Character formula for Lie superalgebras
I agree with the suggestion in the comments for searching the front of the math arXiv (as an entry point), because this is a quite broad and active topic (and i am not sure it can be fully covered within a couple of references). 


However, i think it might be particularly useful to mention: 


* The [Dictionary on Lie Superalgebras](https://arxiv.org/abs/hep-th/9607161v1), by L. Frappat, A. Sciarrino, P. Sorba, sect. 7, p.10-12, where character and supercharacter formulas are given for the classical, basic Lie superalgebras $A(m,n)$, $B(0,n)$, $C(n+1)$.


and also the following papers by S.J Kang :


* [S.J. Kang, Graded Lie Superalgebras and the Superdimension Formula, J. of Alg., v.204, 597-655, 1998](https://core.ac.uk/download/pdf/81208379.pdf),
* [S.J. Kang, J.H. Kwon, Graded Lie Superalgebras, Supertrace Formula, and Orbit Lie Superalgebras, Proc. of the London Math. Soc. v.81, 3, November 2000 , p. 675-724](https://www.cambridge.org/core/journals/proceedings-of-the-london-mathematical-society/article/graded-lie-superalgebras-supertrace-formula-and-orbit-lie-superalgebras/3B6060558C726FF852AAEBAFA0797AE4) (see [here](https://arxiv.org/pdf/math/9809025.pdf) for the arXiv version), where a generalized denominator identity is obtained for a  

$(\Gamma\times\mathcal{A})$-graded Lie superalgebra, where $\Gamma$ is a countable abelian semigroup and $\mathcal{A}$ is a countable abelian group satisfying a certain finiteness condition.


