Local unitary periods and relative discrete series
Jerrod Manford Smith

TL;DR
This paper constructs specific representations in the discrete spectrum of a $p$-adic symmetric space involving unitary groups and general linear groups over quadratic extensions, advancing understanding of automorphic representations.
Contribution
It introduces a method to explicitly construct representations in the discrete spectrum of certain $p$-adic symmetric spaces involving unitary groups.
Findings
Constructed representations in the discrete spectrum of $H \backslash G$
Established connections between unitary periods and discrete series
Enhanced understanding of automorphic representations over $p$-adic fields
Abstract
Let be a -adic field (), let be a quadratic Galois extension of , and let . We construct representations in the discrete spectrum of the -adic symmetric space , where and is a quasi-split unitary group over .
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