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Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras

Bowman, C., Cox, A. ORCID: 0000-0001-9799-3122 and Hazi, A. ORCID: 0000-0001-7264-2211 (2020). Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras. .

Abstract

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these algebras (including as examples the symmetric groups and generalised blob algebras) are tautologically equal to the associated $p$-Kazhdan-Lusztig polynomials, provided that the characteristic is greater than the Coxeter number. We hence give an elementary and more explicit proof of the main theorem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic Hecke algebras, thus solving Libedinsky-Plaza's categorical blob conjecture.

Publication Type: Monograph (Working Paper)
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
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Date Deposited: 09 Sep 2020 12:50
URI: https://openaccess.city.ac.uk/id/eprint/24784
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