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Oriented Temperley--Lieb algebras and combinatorial Kazhdan--Lusztig theory

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arxiv 2212.09402 v3 pith:66AXYN4X submitted 2022-12-19 math.RT math.CO

Chris Bowman , Maud De Visscher , Niamh Farrell , Amit Hazi , Emily Norton This is my paper · ORCID
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keywords algebrascombinatorialkazhdan--lusztigorientedspacestemperley--lieballowsclassical
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We define oriented Temperley--Lieb algebras for classical Hermitian symmetric spaces. This allows us to explain the existence of closed combinatorial formulae for the Kazhdan--Lusztig polynomials for these spaces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Faithful covers of Khovanov arc algebras

    math.RT 2024-11 conditional novelty 8.0 of 10

    The extended Khovanov arc algebra K^m_n is an (|n-m|-1)-faithful cover of the Khovanov arc algebra H^m_n.

  2. Quiver presentations and Schur--Weyl duality for Khovanov arc algebras

    math.RT 2024-11 conditional novelty 7.0 of 10

    The Khovanov arc algebras are fully described by an Ext-quiver with Dyck-path arrows, and loops in that quiver are controlled by faithfulness of the extended arc algebra cover.

  3. Search for a basis of the Temperley-Lieb algebra, using rewriting systems

    math.RT 2025-08 conditional novelty 5.0 of 10

    A convergent rewriting system for the Temperley-Lieb algebra is exhibited whose normal forms are the classical Jones normal forms, but the oriented version's basis claim is left as a conjecture.

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