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Special Functions and the Theory of Group Representations
Abstract
A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.
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Citations
Cited by
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Vourdas, A. (2004) · Reports on Progress in Physics · doi:10.1088/0034-4885/67/3/r03 · Cited by 321
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Camporesi, R. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90120-q · Cited by 257
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“ick rotation of AdSd. The corresponding isometry group is then SO(d−1,2). A discussion of the basic elements of this group and the construction of spectral representations in Hd can be found in refs. [25,26] and [12] whose notations and conventions we will follow. The spectral representation for the renormalized two–p…”
BackgroundTopological field theory and the quantum double of SU(2)
Bais, F. A., & Muller, N. M. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00572-0 · Cited by 57
Metadata
- Authors
- Vilenkin, N.
- Venue
- Translations of Mathematical Monographs
- Publisher
- American Mathematical Society
- Published
- 1968-12-31
- ISSN
- 0065-9282 (ISSN-L)
- 2472-5137
- OpenAlex
- W2128633210
- Cited by
- 2,072
- References
- 0
- FWCI
- 18.39
- Type
- book
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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