BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jacob Bridgeman (Ghent University) DTSTART:20240215T100000Z DTEND:20240215T110000Z DTSTAMP:20260423T035540Z UID:EQuAL/21 DESCRIPTION:Title: I nvertible Bimodule Categories and Generalized Schur Orthogonality\nby Jacob Bridgeman (Ghent University) as part of European Quantum Algebra Lec tures (EQuAL)\n\n\nAbstract\nThe Schur orthogonality relations are a corne rstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new\, readily verifiable condition on the skeletal data for deciding whether a given bimodule category is invert ible and therefore defines a Morita equivalence. Ultimately\, the conditio n arises from Schur orthogonality relations on the characters of the annul ar algebra associated to a module category. As a first application\, we pr ovide an algorithm for the construction of the full skeletal data of the i nvertible bimodule category associated to a given module category\, which is obtained in a unitary gauge when the underlying categories are unitary. As a second application\, we show that our condition for invertibility is equivalent to the notion of MPO-injectivity\, thereby closing an open que stion concerning tensor network representations of string-net models exhib iting topological order. Work with Laurens Lootens and Frank Verstraete. B ased on arXiv: 2211.01947\n LOCATION:https://researchseminars.org/talk/EQuAL/21/ END:VEVENT END:VCALENDAR