Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: $A_n$-series

Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb{R})$ and the symplectic Dirac operator

“…Proof. The proof of this claim for the trivial representation of p instead of the simple metaplectic submodules of the Segal-Shale-Weil representation follows from Theorem 1.3 in [5]. For the Segal-Shale-Weil representation it follows by a straightforward verification of all commutation relations for the Lie algebra g.…”

“…An approach to find precise positions of singular vectors in the representation space can be found in [7], [5], [6]. Let V denote a complex simple highest weight L-module, extended to Pmodule by U acting trivially.…”

Equivariant differential operators on spinors in conformal geometry

“…We shall rely on the following approach to find precise positions of singular vectors in a given representation space, cf. [11], [10] for a detailed exposition. First of all, in the present article V denotes a complex simple finite dimensional L-module, extended to P -module by U acting trivially.…”

“…Another possibility is the application of general formula for the representation action of g given in, e.g. [10]. Now, we shall fix a realization of the twisted complex (semi)simple spinor representation (σ λ , S λ ) of so(p, q, R).…”

“…In the present short article we exploit the general framework of [11], [10], [12], and give a short, self-content and signature of the underlying metric independent classification statement, which can be easily modified and adopted to many analogous problems (e.g. the classification for higher spinor representations).…”