On Decomposition Numbers of Diagram Algebras

Armin Shalile ()
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Armin Shalile: University of Stuttgart, Institute for Algebra and Number Theory

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 587-609 from Springer

Abstract: Abstract In this paper, we survey an algorithm which determines the decomposition numbers of the partition algebra, Brauer algebra and walled Brauer algebra over a field of characteristic 0. The algorithm is based on the action of a set of distinguished elements of the algebra, the so-called Jucys-Murphy elements. We also outline the proof which is remarkably uniform.

Keywords: Diagram algebras; Cellular algebras; Decomposition matrices; 20C30; 20G05 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_26

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DOI: 10.1007/978-3-319-70566-8_26

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