On partition algebras for complex reflection groups

In this paper we study the representation theory of two partition algebras related to complex reflection groups. The colored partition algebras, Pk(n,r) introduced by Bloss [M. Bloss, G-colored partition algebras as centralizer algebras of wreath products, J. Algebra 265 (2003) 690–710] and the algebras, Tk(n,r) introduced by Tanabe [K. Tanabe, On the centralizer algebra of the unitary reflection group G(m,p,n), Nagoya Math. J. 148 (1997) 113–126]. In particular, we describe the decomposition of these algebras in terms of irreducible representations.