Coloured blob algebras

Speaker: Mengfan Lyu 
Affiliation: Western Sydney University

Abstract

In this talk, I will introduce the colored blob algebra $CB_{r,n}$, a multi-parameter generalization of the classical blob algebra that incorporates $r-1$ distinct blob colors. I will begin by defining its diagrammatic basis and the relations that govern it.

The main focus will be on establishing the algebraic foundations of $CB_{r,n}$. In particular, I will show that it arises as a quotient of the cyclotomic Hecke algebra $H_{r,1,n}$. This result extends the well-known relationship between the original blob algebra and the Hecke algebra of type B, situating the colored blob algebra naturally within the broader family of cyclotomic Hecke algebra quotients.

I will also demonstrate that $CB_{r,n}$ is a cellular algebra. This structural property ensures a tractable representation theory and facilitates the explicit construction of its simple modules. The framework developed here opens up new directions for research in diagram algebras, representation theory, and related areas.