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Hermite Functions on Compact Lie Groups, I

โœ Scribed by O. Hijab

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
463 KB
Volume
125
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

The usual formula for Hermite polynomials on (\mathbf{R}^{d}) is extended to a compact Lie group (G), yielding an isometry of (L^{2}\left(G, p_{1}\right)), where (p_{1}) is the heat kernel measure at time one, with a natural completion of the universal enveloping algebra of (G). The existence of such an isometry was first established by (\mathbf{L}). Gross; here we present a simplified proof as well as the explicit form of the isometry. 1994 Academic Press, Inc.

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