Representations of two boundary Hecke and Temperley-Lieb algebras (TBHA and TBTL)
I will discuss classifications, constructions and combinatorics of irreducible and standard modules of TBHA and TBTL. The TBTA is the affine Hecke algebra of type C with arbitrary “unequal” parameters. The TBTL is a quotient of the TBHA by local idempotents (for rank 2 sub root systems). The TBTL has been of interest in statistical mechanics: Heisenberg spin chains with boundaries (de Gier-Nichols). The geometry construction of TBHA-modules (Kato) for unequal parameters is via the exotic nilpotent cone.
Professor Arun Ram, University of Melbourne