The unitary dual of the universal covering group of \(\mathrm{GL}(n,\mathbb{R})\)
The author classifies the irreducible unitary representations of the double cover \(G\) of \(\mathrm{GL}(n,\mathbb{R})\) which do not factor to \(\mathrm{GL}(n,\mathbb{R})\) itself. The methods and techniques are similar to \textit{D. Vogan}'s in his classification of the unitary dual of \(\mathrm{GL}(n,\mathbb{R})\) [Invent. Math. 83, 449--505 (1986; Zbl 0598.22008)]. One finds that just one new building block appears in the unitary dual of \(G\). This is a unipotent representation whose Langlands parameters are obtained from those of a well-known unitary representation of \(\mathrm{GL}(n,\mathbb{R})\) by dividing by two. All unitary representations are then obtained from one of the building blocks by unitary induction and Stein complementary series.
scientific article; zbMATH DE number 4210437
scientific article