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, introduced by Bloss [M. Bloss, G-colored partition algebras as centralizer algebras of wreath products, J. Algebra 265 (2003) 690–710] and the algebras, 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.