FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

December 18, 18:30 ~ 18:50 - Room B12

## Plethysm and lattice point counting

### Thomas Kahle

### Otto-von-Guericke Universität Magdeburg, Germany - thomas.kahle@ovgu.de

We show that the coefficient of the Schur functor $S^\lambda$ in the decomposition of the plethysm $S^\mu(S^k)$ into irreducibles is the solution to a lattice point counting problem. Consequently, for each fixed $\mu$, the solution to this problem is a piecewise quasi-polynomial in $(\lambda,k)$. We show how to use computer algebra to determine this function explicitly when $\mu$ is a partition of 4 or 5. We also discuss asymptotics of the resulting piecewise quasi-polynomials.

Joint work with Mateusz Michalek (Simons Institute, UC Berkeley).