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

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagram-matic 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 the-orem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic quiver Hecke al-gebras, thus solving Libedinsky-Plaza's categorical blob con-jecture.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).