Abstract
Given a net\((\mathfrak{g}_l )\) of finite-dimensional real Lie algebras contracting into a Lie algebra
, a representation\(\hat \pi _J \) of
is constructed explicitly as “limit” of a net (π l ) of representations, each π l being a representation of\(\mathfrak{g}_l \) on a complex Hilbert space ℌ l . Conditions are imposed on the net (π l ) implying that the carrier space of\(\hat \pi _J \) contain a
-stable set of vectors which are analytic for all
, where
is a basis of
. As a corollary, the corresponding result for contractions of representations of simply connected finite-dimensional real Lie groups is derived.
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Communicated by H. Araki
Supported by the Swiss National Science Foundation
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Cattaneo, U., Wreszinski, W. On contraction of Lie algebra representations. Commun.Math. Phys. 68, 83–90 (1979). https://doi.org/10.1007/BF01562543
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DOI: https://doi.org/10.1007/BF01562543