THE SCHROEDINGER MODEL FOR THE MINIMAL REPRESENTATION OF THE INDEFINITE ORTHOGONAL GROUP $O(P,Q)$ by Toshiyuki Kobayashi, Gen Mano ( 9780821847572 )

Item Details

Title:

THE SCHROEDINGER MODEL FOR THE MINIMAL REPRESENTATION OF THE INDEFINITE ORTHOGONAL GROUP $O(P,Q)$

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Format:

Paperback

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ISBN 10:

0821847570

ISBN 13:

9780821847572

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

1 January, 2012

Series:

Memoirs of the AMS No. 1000

Pages:

132

Description:

"Volume 213, number 1000 (first of 5 numbers )."

Synopsis:

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.

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

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