The Grothendieck Ring of a Family of Spherical Categories


Abstract in English

The first author constructed a $q$-parameterized spherical category $sC$ over $mathbb{C}(q)$ in [Liu15], whose simple objects are labelled by all Young diagrams. In this paper, we compute closed-form expressions for the fusion rule of $sC$, using Littlewood-Richardson coefficients, as well as the characters (including a generating function), using symmetric functions with infinite variables.

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