The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q)
著者
書誌事項
The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q)
（Memoirs of the American Mathematical Society, no. 1000）
American Mathematical Society, c2011
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注記
"Volume 213, number 1000 (first of 5 numbers)."
Includes bibliography (p. 125-128), list of symbols and index
内容説明・目次
内容説明
The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.
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