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SUMMARY:Yang-Baxter representations of the infinite symmetric group - Gand
 alf Lechner (Cardiff University)
DTSTART:20170613T133000Z
DTEND:20170613T143000Z
UID:TALK72903@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Yang-Baxter equation (YBE) lies at the heart of many subje
 cts\, including quantum statistical mechanics\, QFT\, knot theory\, braid 
 groups\, and subfactors. In this talk\, I will consider involutive solutio
 ns of the YBE ("R-matrices"). Any such R-matrix defines a representation a
 nd an extremal character of the infinite symmetric group as well as a corr
 esponding tower of subfactors.&nbsp\;<br><br>Using these structures\, I wi
 ll describe how to find all R-matrices up to a natural notion of equivalen
 ce (given by the character and the dimension)\, how to completely paramete
 rize the set of solutions\, and how to decide efficiently whether two give
 n R-matrices are equivalent. Joint work with U. Pennig and S. Wood.<br>
LOCATION:Seminar Room 1\, Newton Institute
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