DATE2023-05-04 16:10-17:00

PLACE數學系館 1F3174教室

SPEAKER劉士瑋 博士(中央研究院數學研究所

TITLEAffine Hecke Algebras and Double Affine Hecke Algebras

ABSTRACT In the Lie theory, the combinatorics and the geometry of Weyl groups are of great importance. They appear notably in the Weyl character formula, the Harish-Chandra isomorphism, and the Schur–Weyl duality. The affine Weyl groups are important for affine Lie algebras for the same reason.
The Iwahori–Hecke algebras, deformations of Weyl groups, are omnipresent in the representation theory. The main objects of the talk are affine Hecke algebras, which are deformations of affine Weyl groups, and double affine Hecke algebras, deformations of double affine Weyl groups.
In this talk, I will explain how these objects arise and what applications they have in Lie theory.