IwahoriHecke

IwahoriHecke refers to a mathematical concept that combines the work of Japanese mathematician Kenji Iwahori and German mathematician Erich Hecke. Specifically, it is most commonly associated with the Iwahori-Hecke algebra, which is a type of algebra that arises in the study of group theory and representation theory.

The Iwahori-Hecke algebra is a deformation of the group algebra of a finite group. It plays a significant role in understanding the representation theory of finite groups and, more generally, of p-adic groups and reductive algebraic groups. The algebra is constructed by introducing a parameter, often denoted by q, which allows for a continuous deformation of the group algebra. This deformation leads to a richer structure and allows for the study of representations that are not present in the original group algebra.

One of the key motivations for studying Iwahori-Hecke algebras comes from their connection to automorphic forms and the Langlands program. These algebras appear naturally in the study of spherical representations of reductive groups over local fields. The structure of the Iwahori-Hecke algebra is often simpler than that of the original group algebra, making it a useful tool for computation and theoretical development. The theory has found applications in various areas of mathematics, including number theory, algebraic geometry, and mathematical physics.