On the Bernstein--Zelevinsky classification in families
Sam Mundy

TL;DR
This paper investigates how admissible representations of p-adic GL_n vary within families, demonstrating the rigidity of ramified parts and exploring applications to GL_n-eigenvarieties.
Contribution
It provides new insights into the Bernstein--Zelevinsky classification's behavior in families and establishes the rigidity of ramified components.
Findings
Ramified parts of families are rigid.
Results applicable to GL_n-eigenvarieties.
Enhanced understanding of representation variation in p-adic groups.
Abstract
We study the variation of admissible representations of -adic in families from the point of view of the Bernstein--Zelevinsky classification and show that the ramified parts of these families are rigid. We explain how to apply our results in the context of -eigenvarieties.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Mathematical Analysis and Transform Methods
