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NT & AG Lunch: Sazzad Biswas "Local gamma factors, and converse problems" | Einstein Institute of Mathematics

NT & AG Lunch: Sazzad Biswas "Local gamma factors, and converse problems"

Date: 
Mon, 19/11/201813:00-14:00
Location: 
Faculty lounge, Math building
Let F be a non-Archimedean local field. In the representation theory of GL_n(F), one of the basic problems is to characterize its irreducible representations up to isomorphism. There are many invariants (e.g., epsilon factors, L-functions, gamma factors, depth, etc) that we can attach to a representation of GL_n(F). Roughly, the local converse problem is to find the smallest subcollection of twisted local \gamma-factors which classifies the
irreducible admissible representations of GL_n(F) up to isomorphism.
Since the local gamma-factor is the main ingredient of the converse problem, first, we will try to understand the local gamma-factors and their properties.
Then we will discuss the local converse theorems and related problems.
Key words: Local fields, Reductive groups, Generic representation, Whittaker model, L- and \epsilon-factors, local gamma factor, Local converse theorem