Explore an advanced mathematics lecture that delves into the study of covers of reductive groups and their relationship to Langlands' functoriality principle. Learn how extensions of complex reductive groups by Galois groups can be interpreted as L-groups of covers of reductive groups, particularly in the context of local base fields. Understand how these covers can emerge from a universal cover of the topological group G(F) through a fundamental group \tilde\pi_1(G). Examine two practical applications: the characterization of local Langlands correspondence for supercuspidal L-parameters with large p, and the construction of transfer factors in endoscopy theory. Building upon Adams-Vogan's work on real groups, discover how these concepts extend to arbitrary local fields.
Overview
Syllabus
Tasho Kaletha | Covers of reductive groups and functoriality
Taught by
Harvard CMSA
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