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arXiv · 2601.04012

The orientifold Temperley--Lieb algebra

Chris Bowman·Zajj Daugherty·Maud De Visscher·Rob Muth·Loic Poulain D'andecy
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Abstract

We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot's orientifold quiver Hecke algebras. We prove that the symplectic blob algebras are graded cellular and provide a conjectural algorithm for calculating their graded decomposition matrices. In doing so, we give the first explicit family of finite-dimensional graded quotients of the orientifold quiver Hecke algebras, providing a new entry point for the structure of these algebras -- in the spirit of Libedinsky--Plaza's ``blob algebra approach'' to modular representation theory.

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BibTeXRIS

Chris Bowman, Zajj Daugherty, Maud De Visscher, Rob Muth, Loic Poulain D'andecy. 2026-01-07. The orientifold Temperley--Lieb algebra. https://arxiv.org/abs/2601.04012

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