The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q)
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Bibliographic Information
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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"Volume 213, number 1000 (first of 5 numbers)."
Includes bibliography (p. 125-128), list of symbols and index
Description and Table of Contents
Description
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.
by "Nielsen BookData"