On the Tensor Product of m-Partition Algebras
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We study the tensor product algebra Pk(x1) ⊗ Pk(x2) ⊗ · · · ⊗ Pk(xm), where Pk(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur–Weyl dualities and also index the inequivalent irreducible representations of the algebra Pk(x1) ⊗ Pk(x2) ⊗ · · · ⊗ Pk(xm) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules.
Abstract
We study the tensor product algebra Pk(x1) ⊗ Pk(x2) ⊗ · · · ⊗ Pk(xm), where Pk(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur–Weyl dualities and also index the inequivalent irreducible representations of the algebra Pk(x1) ⊗ Pk(x2) ⊗ · · · ⊗ Pk(xm) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules.
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