Work

Peter-Weyl Theorem for Iwahori Groups and Highest Weight Categories

Year: 2025

Type: article

Abstract: We study the algebra of functions on the Iwahori group via the category of graded bounded representations of the Iwahori Lie algebra. In particular, we identify the standard and costandard objects in this category with certain generalized Weyl modules. Using this identification we express the characters of the standard and costandard objects in terms of specialized nonsymmetric Macdonald polynomials. We also prove that our category of interest admits a generalized highest weight structure (known as stratified structure). We show, more generally, that such a structure on a category of representations of a Lie algebra implies the Peter-Weyl type theorem for the corresponding algebraic group. In the Iwahori case, standard filtrations of indecomposable projective objects correspond to new “reciprocal” Macdonald-type identities.

Source: Transformation Groups

DOI: 10.1007/s00031-025-09919-x

Authors: Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi, Daniel Orr

Institutions: Tel Aviv University, University of Haifa, Beijing Institute of Mathematical Sciences and Applications, Max Planck Institute for Mathematics, Virginia Tech

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: University of Haifa