The generalized Frobenius-Perron dimension of the polynomial representation ring of U(k), defined as the limit over Verlinde algebra truncations, is exactly the ordinary representation dimension, and the paper proves a new lower bound for Schubert classes in Grassmannian quantum cohomology.
Frobenius-Perron dimensions of integral $\Bbb Z_+$-rings and applications
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abstract
We introduce the notion of the Frobenius-Perron dimension of an integral $\Bbb Z_+$-ring and give some applications of this notion to classification of finite dimensional quasi-Hopf algebras with a unique nontrivial simple module, and of quasi-Hopf and Hopf algebras of prime dimension $p$.
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On Frobenius-Perron Dimension
The generalized Frobenius-Perron dimension of the polynomial representation ring of U(k), defined as the limit over Verlinde algebra truncations, is exactly the ordinary representation dimension, and the paper proves a new lower bound for Schubert classes in Grassmannian quantum cohomology.