Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish an algebra-isomorphism beten the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F. As a by-product  obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category in terms of endomorphisms of the tensor unit of the underlying modular tensor category.
['J. C. Fuchs', 'Ingo Runkel', 'Christoph Schweigert']
I am writing a research paper on a idea The Fusion Algebra of Bimodule Categories
[{"from": "human", "value": "I am writing a research paper on a idea The Fusion Algebra of Bimodule Categories"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish an algebra-isomorphism beten the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F. As a by-product  obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category in terms of endomorphisms of the tensor unit of the underlying modular tensor category."}]