Subhajit Jana, Paul D. Nelson
Published 2019-11-05Version 1
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.
Applications of analytic newvectors for $\mathrm{GL}(r)$
Explicit calculations of automorphic forms for definite unitary groups
On Extension of Ginzburg-Jiang-Soudry Correspondence to Certain Automorphic Forms on $Sp_{4mn}(\BA)$ and $\wt{Sp}_{4mn \pm 2n}(\BA)$
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