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

Autor:	d'Andecy, L. Poulain
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematical Physics Mathematics - Geometric Topology Mathematics - Quantum Algebra
Druh dokumentu:	Working Paper
Popis:	This document is a thesis presented for the ``Habilitation \`a diriger des recherches''. The first chapter provides some background and sketch the story of the classical Schur-Weyl duality and its quantum analogue involving the Hecke algebra. Quantum groups and their centralisers are discussed along with their connections with the braid group, the Yang-Baxter equation and the construction of link invariants. A quick review of several related notions of Hecke algebras concludes the first chapter. The second chapter presents the fused Hecke algebras and an application to the construction of solutions for the Yang-Baxter equation. The third chapter summarises recent works on diagonal centralisers of Lie algebras, and gives an application to the study of the missing label for sl(3). The last chapter discusses algebraic results on the Yokonuma-Hecke algebras and their applications to the study of link invariants. Comment: 81 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.00850 Zobrazit plný text záznamu View this record from Arxiv