Schroedinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ (eBook)

Toshiyuki Kobayashi (Autor)

eBook Download: PDF

132 Seiten
American Mathematical Society (Verlag)
978-1-4704-0617-2 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• ISBN-10: 1-4704-0617-9 / 1470406179
• ISBN-13: 978-1-4704-0617-2 / 9781470406172