|
This article is cited in 76 scientific papers (total in 76 papers)
Highest weight categories arising from Khovanov's diagram algebra I: cellularity
Jonathan Brundana, Catharina Stroppelb a Department of Mathematics, University of Oregon, Eugene, OR, USA
b Department of Mathematics, University of Bonn, Bonn, Germany
Abstract:
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 $K^\infty_m$, $K^{\pm\infty}_m$ and $K^\infty_\infty$. 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 $H^n_m$, $K^n_m$ and $K^\infty_m$ to level two blocks of degenerate cyclotomic Hecke algebras, parabolic category $\mathcal O$ and the general linear supergroup, respectively.
Key words and phrases:
highest weight category, cellular algebra, diagram algebra.
Received: July 15, 2009; in revised form January 25, 2011
Citation:
Jonathan Brundan, Catharina Stroppel, “Highest weight categories arising from Khovanov's diagram algebra I: cellularity”, Mosc. Math. J., 11:4 (2011), 685–722
Linking options:
https://www.mathnet.ru/eng/mmj439 https://www.mathnet.ru/eng/mmj/v11/i4/p685
|
Statistics & downloads: |
Abstract page: | 444 | References: | 65 |
|