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 $\lambda /\mu$.

arXiv commentThe paper has been withdrawn by the authors.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

References in corpus (1)

• On representations of the Lie superalgebra p(n)