The orientifold Temperley--Lieb algebra
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911358850695168 |
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| author | Bowman, Chris Daugherty, Zajj De Visscher, Maud Muth, Rob D'andecy, Loic Poulain |
| author_facet | Bowman, Chris Daugherty, Zajj De Visscher, Maud Muth, Rob D'andecy, Loic Poulain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The orientifold Temperley--Lieb algebra Bowman, Chris Daugherty, Zajj De Visscher, Maud Muth, Rob D'andecy, Loic Poulain Representation Theory Mathematical Physics Combinatorics Quantum Algebra 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. |
| title | The orientifold Temperley--Lieb algebra |
| topic | Representation Theory Mathematical Physics Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2601.04012 |