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- W4283395551 abstract "Let ${mathfrak g}$ denote the complexified Lie algebra of $G={mathrm O}(p,q)$ and $K$ a maximal compact subgroup of $G$. In the previous paper, we constructed $({mathfrak g},K)$-modules associated to the finite-dimensional representation of ${mathfrak sl}_2$ of dimension $m+1$, which we denote by $M^{+}(m)$ and $M^{-}(m)$. The aim of this paper is to show that the annihilator of $M^{pm}(m)$ is the Joseph ideal if and only if $m=0$. We shall see that an element of the symmetric of square $S^{2}({mathfrak g})$ that is given in terms of the Casimir elements of ${mathfrak g}$ and the complexified Lie algebra of $K$ plays a critical role in the proof of the main result." @default.
- W4283395551 created "2022-06-25" @default.
- W4283395551 creator A5045431309 @default.
- W4283395551 date "2022-06-22" @default.
- W4283395551 modified "2023-09-29" @default.
- W4283395551 title "Annihilator of $({mathfrak g},K)$-modules of ${mathrm O}(p,q)$" @default.
- W4283395551 doi "https://doi.org/10.48550/arxiv.2206.10854" @default.
- W4283395551 hasPublicationYear "2022" @default.
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