the kodoku(na) projector the notes for this talk are not here yet. but in a nutshell it simply notes the use of the Chi projector from [M95] in various guises such as [MM13a], dilute TL and so on. [MM13a] P. P. Martin and V. Mazorchuk. On the representation theory of partial Brauer algebras The Quarterly Journal of Mathematics (2013); doi: 10.1093/qmath/has043