Subrings of the asymptotic Hecke algebra of type $H_4$

Dean Alvis

Subrings of the asymptotic Hecke algebra of type $H_4$

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arxiv 0705.0528 v2 pith:THH6D2Q3 submitted 2007-05-03 math.RT math.RA

Dean Alvis This is my paper · ORCID

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abstract

The structure of subring $J^{\Gamma \cap \Gamma^{-1}}$ of the asymptotic Hecke algebra is described for $\Gamma$ a left cell of the Coxeter group of type $H_4$. A small set of generators is produced. The subalgebras spanned by a subset of the basis ${t_x}_{x\in \Gamma\cap\Gamma^{-1}}$ are determined.

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Idempotents, traces, and dimensions in Hecke categories
math.RT 2025-07 conditional novelty 8.0 of 10

The paper provides closed formulas for recursible local intersection forms and recursive partial trace formulas that reduce categorical dimensions in asymptotic Hecke categories to diagrammatic computations.

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