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

By A. Cox, M. Visscher. 2010

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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–Schutzenberger and Boe, inspired by work of Brundan and Stroppel in the cap diagram case.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/559d91293ab2ca1ad3656d70abc11e945c15728d