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The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group O (P,q): 1000 (Memoirs of the American Mathematical Society)

Algebra

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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. About the Author Toshiyuki Kobayashi is at University of Tokyo, Japan||PricewaterhouseCoopers Aarata, Tokyo, Japa

Product Specifications

Format: paperback
ASIN: 0821847570
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 29 August 2011
Listed Since: 10 June 2011

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The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group O (P,q): 1000 (Memoirs of the American Mathematical Society)

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