  We construct combinatorial (involutory) Gelfand models for the following
diagram algebras in the case when they are semi-simple: Brauer algebra, its
partial analogue, walled Brauer algebra, its partial analogue, Temperley-Lieb
algebra, its partial analogue, walled Temperley-Lieb algebra, its partial
analogue, partition algebra and its Temperley-Lieb analogue.
