Branching laws for small unitary representations of GL(n,C)

Abstract

The unitary principal series representations of $G=GL(n,\mathbb{C})$ induced from a character of the maximal parabolic subgroup $P=(GL(1,\mathbb{C})\times GL(n-1,\mathbb{C}))⋉{\mathbb{C}}^{n-1}$ attain the minimal Gelfand--Kirillov dimension among all infinite-dimensional unitary representations of $G$. We find the explicit branching laws for the restriction of these representations to symmetric subgroups of $G$.

14 pages

References in corpus (3)

• Structure of the degenerate principal series on symmetric R-spaces and small representations
• Algebraic analysis of minimal representations
• Branching laws for discrete Wallach points