Research

Mathematical Sciences

Title :

Hecke algebras for tame Bernstein blocks

Area of research :

Mathematical Sciences

Focus area :

Mathematics

Principal Investigator :

Dr. Manish Kumar Mishra, Associate Professor, Indian Institute of Science Education and Research, Pune

Timeline Start Year :

2023

Contact info :

Details

Executive Summary :

The Langlands program is a mathematical theory that organizes fundamental arithmetic objects in terms of automorphic representations. It was formulated in 1967 by Robert Langlands and is a specialization of the Bushnell-Kutzko theory. The local Langlands conjecture (LLC) states that irreducible admissible objects of the category R(G(F)) can be partitioned into finite sets called L-packets. The category decomposes into Bernstein blocks, equivalent to the module category of an assciative C-algebra called Hecke algebra. The project aims to complete the Bushnell-Kutzko program and specialize the result to principal series blocks.

Total Budget (INR):

29,68,888

Organizations involved