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arXiv · 1009.4064

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

Anton Cox·Maud De Visscher
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Abstract

We determine the decomposition numbers for the Brauer and walled Brauer algebra 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.

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Anton Cox, Maud De Visscher. 2010-09-21. Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra. https://arxiv.org/abs/1009.4064

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