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Cahen, Benjamin

Contraction of compact semisimple Lie groups via Berezin quantization. (English) Zbl 1185.22008

Ill. J. Math. 53, No. 1, 265-288 (2009).
This paper establishes contractions of a compact semisimple Lie group. Let us recall that contractions of Lie groups have been introduced by Inonu and Wigner for physical purposes. Generally speaking, contraction theory is a way to relate the harmonic analysis on two Lie groups and enables one to recover as a byproduct the properties of special functions. In this paper, the author concentrates on the contractions of the unitary irreducible representations of a compact semisimple Lie group to the unitary irreducible representations of a Heisenberg group. The Berezin calculus is then introduced and related to the contraction of the Lie groups. Finally, the example of \(G= \text{SU}(p+q)\) is studied.
Reviewer: Angela Gammella-Mathieu (Metz)

Cited in 7 Documents

MSC:

22E46 Semisimple Lie groups and their representations
81R30 Coherent states
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

contraction of Lie groups; harmonic analysis; representation theory; Berezin quantization; Heisenberg group
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\textit{B. Cahen}, Ill. J. Math. 53, No. 1, 265--288 (2009; Zbl 1185.22008)
Full Text: Euclid

References:

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