Structure of Twisted Jacquet Modules for GL(2n)
Published:Dec 31, 2025 09:11
•1 min read
•ArXiv
Analysis
This paper investigates the structure of twisted Jacquet modules of principal series representations of GL(2n) over a local or finite field. Understanding these modules is crucial for classifying representations and studying their properties, particularly in the context of non-generic representations and Shalika models. The paper's contribution lies in providing a detailed description of the module's structure, conditions for its non-vanishing, and applications to specific representation types. The connection to Prasad's conjecture suggests broader implications for representation theory.
Key Takeaways
- •Provides a detailed description of the structure of twisted Jacquet modules for principal series representations of GL(2n).
- •Establishes necessary and sufficient conditions for the twisted Jacquet module to be non-zero.
- •Applies the results to understand the structure of twisted Jacquet modules for certain non-generic irreducible representations.
- •Connects the findings to the existence of Shalika models.
- •Concludes with a discussion of Prasad's conjecture on the classification of representations with non-zero twisted Jacquet modules.
Reference
“The paper describes the structure of the twisted Jacquet module π_{N,ψ} of π with respect to N and a non-degenerate character ψ of N.”