English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This document is a thesis presented for the ``Habilitation \`a diriger desrecherches''. The first chapter provides some background and sketch the storyof the classical Schur-Weyl duality and its quantum analogue involving theHecke algebra. Quantum groups and their centralisers are discussed along withtheir connections with the braid group, the Yang-Baxter equation and theconstruction of link invariants. A quick review of several related notions ofHecke algebras concludes the first chapter. The second chapter presents thefused Hecke algebras and an application to the construction of solutions forthe Yang-Baxter equation. The third chapter summarises recent works on diagonalcentralisers of Lie algebras, and gives an application to the study of themissing label for sl(3). The last chapter discusses algebraic results on theYokonuma-Hecke algebras and their applications to the study of link invariants.

Centralisers and Hecke algebras in Representation Theory, with applications to Knots and Physics