Invariant tensors and cellular categories

Abstract

Let U be the quantised enveloping algebra associated to a Cartan matrix of finite type. Let W be the tensor product of a finite list of highest weight representations of U. Then the centraliser algebra of W has a basis called the dual canonical basis which gives an integral form. We show that this integral form is cellular by using results due to Lusztig.

6 pages; to appear in Journal of Algebra

References in corpus (1)

• Invariant tensors for the spin representation of so(7)

Cited by in corpus (12)

• Cellular structures using ${\text{U}}_q$-tilting modules
• Semi-infinite highest weight categories
• Light ladders and clasp conjectures
• Trace decategorification of the Hecke category
• Modular representation theory in type A via Soergel bimodules
• SL2 tilting modules in the mixed case
• Web bases for the general linear groups
• Radicals of symmetric cellular algebras
• Soergel bimodules for universal Coxeter groups
• Jucys-Murphy elements for Soergel bimodules
• Graded triangular bases
• On rank one 2-representations of web categories