Handlebody diagram algebras

Abstract

In this paper we study handlebody versions of some classical diagram algebras, most prominently, handlebody versions of Temperley-Lieb, blob, Brauer, BMW, Hecke and Ariki-Koike algebras. Moreover, motivated by Green-Kazhdan-Lusztig's theory of cells, we reformulate the notion of (sandwich, inflated or affine) cellular algebras. We explain this reformulation and how all of the above algebras are part of this theory.

45 pages, lots of figures, revision following referees comments, to appear in Rev. Mat. Iberoam, comments welcome

References in corpus (5)

• The two-boundary Temperley-Lieb algebra
• Super $q$-Howe duality and web categories
• The Cyclotomic Birman-Murakami-Wenzl Algebras
• Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras
• DG-Enhanced Hecke and KLR Algebras