Tilting Modules for the Symplectic Blob Algebra

Abstract

Let $\Field$ be an algebraically closed field. For $n\in \mathbb{N}$ and $δ, δ_L, δ_R, κ_L, κ_R, κ\in \Field$, the symplectic blob algebra $\sba(δ, δ_L, δ_R, κ_L, κ_R, κ)$ is a finite dimensional non-commutative $\Field$-algebra that may be viewed as an extension of the Temperley-Lieb algebra. In a previous paper, we defined, for any $n\in \mathbb{N}$, a tensor space module $\tensor[_\sba]{\mathcal{V}(n)}{}$. In this paper we generalise an argument used by Martin and Ryom-Hansen in their study of the (ordinary) blob algebra to show that when $\sba$ is quasihereditary the module $\tensor[_\sba]{\mathcal{V}(n)}{}$ is full-tilting.

24 pages

References in corpus (4)

• The two-boundary Temperley-Lieb algebra
• The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models
• On the non-generic representation theory of the symplectic blob algebra
• A Tensor Space Representation of the Symplectic Blob Algebra

Cited by in corpus (4)

• How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models
• Calibrated representations of two boundary Temperley-Lieb algebras
• On quasi-heredity and cell module homomorphisms in the symplectic blob algebra
• Decomposition matrices and blocks for the symplectic blob algebra over the complex field