Ribbon tiling and character formula for periplectic Lie superalgebras

Abstract

We give a combinatorial formula for the character of a finite-dimensional irreducible representation of the periplectic Lie superalgebra $\mathfrak{p}(n)$. The character of irreducible module $L(\mu )$ is given by a cancellation-free alternating sum over the characters of thick or thin Kac modules, $\Delta (\lambda )$ or $\nabla (\lambda )$, such that there exists a ribbon tiling of a skew Young diagram $\lambda /\mu$.

The paper has been withdrawn by the authors. There is an error in Lemma 3.4, which plays a crucial role in the proof of Theorems 3.11 and 3.14. The authors thank Shifra Reif and Mee Seong Im for correspondence which led them to find this error