The recollement approach to the representation theory of sequences ofalgebras is extended to pass basis information directly through theglobalisation functor. The method is hence adapted to treat sequences that arenot necessarily towers by inclusion, such as symplectic blob algebras (diagramalgebra quotients of the type-$\hati{C}$ Hecke algebras). By carefully reviewing the diagram algebra construction, we find a new set offunctors interrelating module categories of ordinary blob algebras (diagramalgebra quotients of the type-${B}$ Hecke algebras) at {\em different} valuesof the algebra parameters. We show that these functors generalise to determinethe structure of symplectic blob algebras, and hence of certain two-boundaryTemperley-Lieb algebras arising in Statistical Mechanics. We identify the diagram basis with a cellular basis for each symplectic blobalgebra, and prove that these algebras are quasihereditary over a field foralmost all parameter choices, and generically semisimple. (That is, we givebases for all cell and standard modules.)
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