Multiplet Classification of Reducible Verma Modules over the $G_2$ Algebra

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $G_{2(2)}$ which is split real form of $G_2$. We give the classification of reducible Verma modules $G_2$. We give also the singular vectors between these modules, thus setting the stage for construction of the invariant differential operators over $G_{2(2)}$.

arXiv comment9 pages, 7 figures, Invited talk at the XXXII International Colloquium on Group Theoretical Methods in Physics (Prague, July 2018); session dedicated to I.E. Segal (1918-1998)

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Cited by in corpus (2)

• Heisenberg Parabolic Subgroups of Exceptional Noncompact $G_{2(2)}$ and Invariant Differential Operators
• An exceptional symmetry algebra for the 3D Dirac-Dunkl operator