On Frobenius-Perron Dimension

Abstract

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.

References in corpus (3)

• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Conformal blocks, fusion rules and the Verlinde formula
• Frobenius-Perron Theory of Modified ADE Bound Quiver Algebras