Branching laws for small unitary representations of GL(n, ℂ) - Möllers, Jan; Schwarz, Benjamin (International Journal of Mathematics, 2014)
The unitary principal series representations of G = GL(n, ℂ) induced from a character of the maximal parabolic subgroup P = (GL(1, ℂ) × GL(n - 1, ℂ)) ⋉ ℂn-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 all reductive subgroups H of G such that (G, H) forms a symmetric pair.
Keywords: Small representation; branching law; symmetric pair; degenerate principal series; Plancherel formula