On geometrically defined extensions of the Temperley-Lieb category in the Brauer category

Abstract

We define an infinite chain of subcategories of the partition category by introducing the left-height ($l$) of a partition. For the Brauer case, the chain starts with the Temperley-Lieb ($l=-1$) and ends with the Brauer ($l=\infty$) category. The End sets are algebras, i.e., an infinite tower thereof for each $l$, whose representation theory is studied in the paper.

28 pages

References in corpus (5)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• The Cyclotomic Birman-Murakami-Wenzl Algebras
• The decomposition matrices of the Brauer algebra over the complex field
• Pascal arrays: counting Catalan sets
• A Temperley-Lieb category for 2-manifolds

Cited by in corpus (1)

• Geometric partition categories: On short Brauer algebras and their blob subalgebras