Tautological p-Kazhdan-Lusztig Theory for Cyclotomic Hecke Algebras

Explore an advanced mathematics lecture on tautological p-Kazhdan-Lusztig Theory for cyclotomic Hecke algebras. Delve into a new explicit isomorphism between truncations of quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. Discover how this isomorphism leads to the conclusion that decomposition numbers of these algebras, including symmetric groups and generalised blob algebras, are tautologically equal to associated p-Kazhdan-Lusztig polynomials when the characteristic exceeds the Coxeter number. Examine an elementary and explicit proof of the main theorem from Riche-Williamson's recent monograph, and learn how their categorical equivalence extends to cyclotomic Hecke algebras, resolving Libedinsky-Plaza's categorical blob conjecture.