On Frobenius-Perron Dimension
Changzheng Li, Ryan M. Shifler, Mingzhi Yang, Chi Zhang

TL;DR
This paper introduces a new Frobenius-Perron dimension concept for infinite rank modules, computes it for certain representation modules, and establishes bounds for quantum cohomology classes in Grassmannians.
Contribution
It defines Frobenius-Perron dimension for infinite rank modules and computes it for specific representation modules, also providing bounds in quantum cohomology.
Findings
Frobenius-Perron dimension for certain infinite modules is defined and computed.
Explicit Frobenius-Perron dimensions are obtained for complex representations of unitary groups.
A lower bound for Frobenius-Perron dimensions of Schubert classes in quantum cohomology is established.
Abstract
We propose a notion of Frobenius-Perron dimension for certain free -modules of infinite rank and compute it for the -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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra
