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arXiv · 1911.01880

Analytic newvectors for $\mathrm{GL}_n(\mathbb{R})$

Subhajit Jana·Paul D. Nelson
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Abstract

We relate the analytic conductor of a generic irreducible representation of $\mathrm{GL}_n(\mathbb{R})$ to the invariance properties of vectors in that representation. The relationship is an analytic archimedean analogue of some aspects of the classical non-archimedean newvector theory of Casselman and Jacquet--Piatetski-Shapiro--Shalika. We illustrate how this relationship may be applied in trace formulas to majorize sums over automorphic forms on $\mathrm{PGL}_n(\mathbb{Z}) \backslash \mathrm{PGL}_n(\mathbb{R})$ ordered by analytic conductor.

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Subhajit Jana, Paul D. Nelson. 2019-11-05. Analytic newvectors for $\mathrm{GL}_n(\mathbb{R})$. https://arxiv.org/abs/1911.01880

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