On Frobenius-Perron Dimension

4 Sep 2019 · Changzheng Li, Ryan M. Shifler, Mingzhi Yang, Chi Zhang ·

We propose a notion of Frobenius-Perron dimension for certain free $\mathbb{Z}$-modules of infinite rank and compute it for the $\mathbb{Z}$-modules of finite dimensional complex representations of unitary groups with nonnegative dominant weights. We also provide a lower bound for the Frobenius-Perron dimension of Schubert classes in the quantum cohomology of complex Grassmannians.