Semi-simplicity of Temperley-Lieb Algebras of type D

Abstract

We provide a necessary and sufficient condition for a type D Temperley-Lieb algebra ${\mathrm{TLD}}_n(\delta )$ being semi-simple by studying branching rule for cell modules. As a byproduct, our result is used to study the so-called forked Temperley-Lieb algebra, which is a quotient algebra of ${\mathrm{TLD}}_n(\delta )$.

26 pages

References in corpus (2)

• Representations of Temperley--Lieb Algebras
• The Dieck-Temperley-Lieb algebras in Brauer algebras