Highest weight categories arising from Khovanov's diagram algebra I: cellularity

Details Highest weight categories arising from Khovanov's diagram algebra I: cellularity Highest weight categories arising from Khovanov's diagram algebra I: cellularity

2008-06-09

arxiv.org/abs/0806.1532v3

Mosc. Math. J. 11 (2011), 685-722

Mathematics

Representation Theory

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Scientific paper

This is the first of four articles studying some slight generalisations H(n,m) of Khovanov's diagram algebra, as well as quasi-hereditary covers K(n,m) of these algebras in the sense of Rouquier, and certain infinite dimensional limiting versions. In this article we prove that H(n,m) is a cellular symmetric algebra and that K(n,m) is a cellular quasi-hereditary algebra. In subsequent articles, we relate these algebras to level two blocks of degenerate cyclotomic Hecke algebras, parabolic category O and the general linear supergroup, respectively.

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