## Student Number Theory Seminar 2019-20

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3/30/20: Emily Tibor -- *Introduction to Klyachko Models for GL_n*

**Abstract:** Whittaker models for representations of GL_n have been featured in a number of student number theory seminar talks this year. In this talk, I will introduce a generalization of this model, called Klyachko models, which are mixed Whittaker-symplectic models, and discuss their properties. I will begin by recalling Whittaker models and their significance, which will lead into a more general discussion of why one might be interested in the study of unique models. Then, I will introduce Klyachko models for GL_n and explore questions about their existence and uniqueness over finite and non-Archimedean local fields.