Representation theory and cellular structure of seam algebras

by Alexis Langlois Rémillard (Ghent University)

Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday June 7, 2019 at 14:30

The seam algebras were introduced by Morin-Duchesne, Rasmussen and Ridout (2015) in order to introduce an adequate algebraic framework for the lattice analysis in Kac modules and their continuum limit counterpart, the Virasoro-Kac modules. They were viewed there as quotients of one-boundary Temperley-Lieb algebras and they were proven semisimple for generic value of the loop fugacity were given. It was known that they could also be obtained from classical Temperley-Lieb algebra by acting with a family of idempotents. Using this fact, we constructed a cellular basis for the seam algebra by exploiting the properties of a restriction functor and found complete sets of irreducible and principal modules for all the non-semisimple cases, except for one elusive family. This is joint work with Yvan Saint-Aubin.

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