The partition algebra CAk (n) is the centralizer algebra of Sn acting on the k-fold tensor
product V⊗ k of its n-dimensional permutation representation V. The partition algebra CAk+ …

The partition algebra P (q) is a generalization both of the Brauer algebra and the Temperley–
Lieb algebra for q-state n-site Potts models, underpining their transfer matrix formulation on …

The partition algebra is an associative algebra with a basis of set-partition diagrams and
multiplication given by diagram concatenation. It contains as subalgebras a large class of …

We extend the calculus of relations to embed a regular category A into a family of pseudo-
abelian tensor categories T (A, δ) depending on a degree function δ. Assume that all objects …

The partition algebra P _k (n) P k (n) and the symmetric group S _n S n are in Schur–Weyl
duality on the k-fold tensor power M _n^ ⊗ k M n⊗ k of the permutation module M _n M n of S …

For each natural number n, poset T, and| T|–tuple of scalars Q, we introduce the ramified
partition algebra (Q), which is a physically motivated and natural generalization of the …

Affine and periodic Temperley-Lieb algebras are families of diagrammatic algebras that find
diverse applications in mathematics and physics. These algebras are infinite-dimensional …

We describe various diagram algebras and their representation theory using cellular
algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we …

The localisation functor is directly analogous to the Schur functor, and provides a powerful
tool for the transfer of information from the Schur algebras to the partition algebras. In …

The rook partition algebra RPk (x) is a generically semisimple algebra that arises from
looking at what commutes with the action of the symmetric group Sn on U⊗ k, where U is the …