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Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra

Cox, A. and De Visscher, M. (2011). Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra. Journal of Algebra, 340(1), pp. 151-181. doi: 10.1016/j.jalgebra.2011.05.024

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.

Publication Type: Article
Publisher Keywords: Brauer algebra, Kazhdan-Lusztig polynomial, CENTRALIZER ALGEBRAS, POLYNOMIALS, REPRESENTATIONS, GRASSMANNIANS, BLOCKS
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/368
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