Abstract

We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type (C) over tilde, namely, the two-boundary Temperley-Lieb algebra and the symplectic blob algebra. We provide a monomial basis for both algebras. The elements of these bases are parameterized by certain subsets of fully commutative elements. We enumerate these elements according to their affine length. (C) 2021 Elsevier Inc. All rights reserved.