On the degenerate principal series of $G_{2(2)}$ induced from a Heisenberg parabolic subgroup

Jan Frahm; Robin van Haastrecht; Clemens Weiske; Genkai Zhang

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arXiv · 2601.20344

On the degenerate principal series of $G_{2(2)}$ induced from a Heisenberg parabolic subgroup

Jan Frahm·Robin van Haastrecht·Clemens Weiske·Genkai Zhang

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Abstract

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. Using the Lie algebra action on the space of $K$-finite vectors, we find the points of reducibility and the complementary series. The minimal representation and a limit of discrete series are identified as kernel of the corresponding Knapp-Stein intertwining operator. Moreover, we show that some quaternionic discrete series representations occur as the subrepresentation on which the family of intertwining operators vanishes of order two.

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Jan Frahm, Robin van Haastrecht, Clemens Weiske, Genkai Zhang. 2026-01-28. On the degenerate principal series of $G_{2(2)}$ induced from a Heisenberg parabolic subgroup. https://arxiv.org/abs/2601.20344

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