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arXiv · 0808.3405

The SL(2)-type and Base Change

Omer Offen·Eitan Sayag
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Abstract

The SL(2)-type of any smooth, irreducible and unitarizable representation of GL(n) over a p-adic field was defined by Venkatesh. We provide a natural way to extend the definition to all smooth and irreducible representations. For unitarizable representations we show that the SL(2)-type of a representation is preserved under base change with respect to any finite extension. The Klyachko model of a smooth, irreducible and unitarizable representation πof GL(n) depends only on the SL(2)-type of π. As a consequence we observe that the Klyachko model of πand of its base-change are of the same type.

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Omer Offen, Eitan Sayag. 2008-08-25. The SL(2)-type and Base Change. https://arxiv.org/abs/0808.3405

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