Principal series representations of Iwahori-Hecke algebras for Kac-Moody groups over local fields

Abstract: Let G be a split reductive group over a non-Archimedean local field and H be its Iwahori-Hecke algebra. Principal series representations of H, introduced by Matsumoto at the end of 1970's, are important in the representation theory of H. Every irreducible representation of H is the quotient of and can be embedded in some principal series representation of H and thus studying these representations enables to get information on the irreducible representations of H. S.Kato provided an irreducibility criterion for these representations in the beginning of the 1980's.

Kac-Moody groups are interesting infinite dimensional generalizations of reductive groups. Their study over non-Archimedean local field began in 1995 with the works of Garland. Let G be a split Kac-Moody group (à la Tits) over a non-Archimedean local field. Braverman, Kazhdan and Patnaik and Bardy-Panse, Gaussent and Rousseau associated an Iwahori-Hecke algebra to G in 2014. I recently defined principal series representations of these algebras. In this talk, I will talk of these representations, of a generalization of Kato's irreducibility criterion for these representations and of how they decompose when they are reducible.

number theoryrepresentation theory

Audience: researchers in the topic

Geometry, Number Theory and Representation Theory Seminar