Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The Modular Generalized Springer Correspondence (MGSC), as developed by Achar, Juteau, Henderson, and Riche, stands as a significant extension of the early groundwork laid by Lusztig's Springer Correspondence in characteristic zero which provided crucial insights into the representation theory of finite groups of Lie type. Building upon Lusztig's work, a generalized version of the Springer Correspondence was later formulated to encompass broader contexts.

In the realm of modular representation theory, Juteau's efforts gave rise to the Modular Springer Correspondence, offering a framework to explore the interplay between algebraic geometry and representation theory in positive characteristic. Achar, Juteau, Henderson, and Riche further extended this correspondence to encompass a more expansive range of phenomena, culminating in the development of the Generalized Modular Springer Correspondence. In their series of papers, they describe explicityly the correspondence for a number of linear algebraic groups, in parti. The goal of this paper is to finish their work for the case when k">kk is a field of positive characteristic ℓ≠2">ℓ≠2ℓ≠2 . The case when ℓ=2">ℓ=2ℓ=2 was treated in \cite{Achar_20172}.

Date

4-4-2024

Committee Chair

Achar, Pramod

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