Cox, A. & De Visscher, M. (2011). Diagrammatic KazhdanLusztig theory for the (walled) Brauer algebra. Journal of Algebra, 340(1), pp. 151181. doi: 10.1016/j.jalgebra.2011.05.024

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Abstract
We determine the decomposition numbers for the Brauer and walled Brauer algebras in characteristic zero in terms of certain polynomials associated to cap and curl diagrams (recovering a result of Martin in the Brauer case). We consider a second family of polynomials associated to such diagrams, and use these to determine projective resolutions of the standard modules. We then relate these two families of polynomials to Kazhdan–Lusztig theory via the work of Lascoux–Schützenberger and Boe, inspired by work of Brundan and Stroppel in the cap diagram case.
Item Type:  Article 

Uncontrolled Keywords:  Brauer algebra, KazhdanLusztig polynomial, CENTRALIZER ALGEBRAS, POLYNOMIALS, REPRESENTATIONS, GRASSMANNIANS, BLOCKS 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/368 
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