TL;DR
This paper establishes a canonical correspondence between certain representation types of GL(n) over local fields and their Langlands parameters, leading to the construction of canonical beta-extensions.
Contribution
It introduces a normalized comparison between representation types and Langlands parameters, enabling the construction of canonical beta-extensions of maximal simple characters.
Findings
Established a normalized comparison between level zero parts and tame Langlands parameters.
Constructed canonical beta-extensions of maximal simple characters.
Provided a framework linking representation theory and Langlands correspondence.
Abstract
We compare the level zero part of the type of a representation of GL(n) over a non-archimedean local field with the tame part of its Langlands parameter restricted to inertia. By normalizing this comparison, we construct canonical -extensions of maximal simple characters.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Topics in Algebra