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 $\lambda/\mu$.