James Parkinson (Sydney University)
TITLE /听TITRE
On Lusztig's Asymptotic Algebra (in affine type A)
听
ABSTRACT /听R脡SUM脡
Kazhdan-Lusztig theory plays a fundamental role in the representation theory of Coxeter groups, Hecke algebras, groups of Lie type, and algebraic groups. One of the most fascinating objects in the theory is the "asymptotic Hecke algebra" introduced by Lusztig in 1987. This algebra is "simpler" than the associated Hecke algebra, yet still encapsulates essential features of the representation theory. This apparent simplicity is somewhat offset by the considerable difficulty one faces in explicitly realising the asymptotic algebra for a given Coxeter group, because on face value it requires a detailed understanding of the entire Kazhdan-Lusztig basis, and the structure constants with respect to this basis. A significant part of this talk will be a gentle introduction to the basic setup of Kazhdan-Lusztig theory (the Kazhdan-Lusztig basis, cells, and the asymptotic algebra). We will then report on a new approach (joint with N. Chapelier, J. Guilhot, and E. Little) to construct the asymptotic algebra for affine type A, focusing on some of the main novelties of this approach, including the notion of a balanced system of cell modules, combinatorial formulae for induced representations, and an asymptotic version of Opdam's Plancherel Theorem.
PLACE /听LIEU
Hybride - UQAM Salle / Room PK-5115, Pavillon Pr茅sident-Kennedy
ZOOM