2.00 pm, Seminar Hall On representation theory of partition algebras for complex reflection groups Ashish Mishra Visiting professor, Universidade Federal do Para. 170119 Abstract In this talk, we define the partition algebra, denoted by T_{k}(r,p,n), for complex reflection group G(r,p,n) acting on the kfold tensor product of the reflection representation C^n of G(r,p,n). A basis of the centralizer algebra of this action of G(r,p,n) was given by Tanabe and for p=1, the corresponding partition algebra was studied by Orellana. We also define a subalgebra T_{k+1/2}(r,p,n) and establish this subalgebra as partition algebra of a subgroup of G(r,p,n) acting on the kfold tensor product of C^n. We call the algebras T_{k}(r,p,n) and T_{k+1/2}(r,p,n) as Tanabe algebras. Our aim is to study the representation theory of Tanabe algebras: parametrization of their irreducible modules by studying the decomposition of the kfold tensor product of C^n as a G(r,p,n)module, and construction of Bratteli diagram for the tower of Tanabe algebras. We also describe JucysMurphy elements of Tanabe algebras and their actions on the GelfandTsetlin basis, determined by the multiplicityfree tower, of irreducible modules.
