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

Kobayashi, Toshiyuki; Mano, Gen

Softcover

ISBN 10: 0821847570 ISBN 13: 9780821847572

Publisher: American Mathematical Society, 2011

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.

About this title

About the Author

Toshiyuki Kobayashi is at University of Tokyo, Japan||PricewaterhouseCoopers Aarata, Tokyo, Japa

Edition details

• Publisher: American Mathematical Society
• Publication date: 2011
• Language: English
• ISBN 10: 0821847570
• ISBN 13: 9780821847572
• Binding: Paperback
• Number of pages: 132