**Data**

- Title: Cellular structures using -tilting modules
- Authors: Henning Haahr Andersen, Catharina Stroppel and Daniel Tubbenhauer
- Status: Pacific J. Math. 292-1 (2018), 21-59. Last update: Mon, 2 Oct 2017 13:46:03 GMT
- ArXiv link: http://arxiv.org/abs/1503.00224
- ArXiv version = 0.99 published version
- LaTex Beamer presentation: Slides1, Slides2, Slides3
- Additional file: File

**Abstract**

**A few extra words**

- The group algebras of the symmetric group and its corresponding Iwahori-Hecke algebra .
- related algebras like Temperley-Lieb algebras and others.
- Spider algebras in the sense of Kuperberg.
- The group algebras of the complex reflection groups and its corresponding Ariki-Koike algebra . In particular, Hecke algebras of type .
- Algebras related to , e.g. (quantum) rook monoid algebras and blob algebras .
- Brauer algebras and its quatazation, the BMW algebras .
- Algebras related to , e.g. walled Brauer algebras .
- More...

- Generalized Khovanov arc algebras.
- -web algebras.
- Cyclotomic Khovanov-Lauda Rouquier algebras of type .
- -algebras.
- More... Our construction of cellular bases is explicit and can be illustrated in a “bow-tie” diagram. Moreover, for the Temperley-Lieb we obtain the so-called “generalized Jones-Wenzl projectors” as basis elements, e.g. (up to a scalar) such a projector looks like: