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Transactions of the American Mathematical Society

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On the integrable and square-integrable representations of $ {\rm Spin}(1, 2m)$


Author: Ernest Thieleker
Journal: Trans. Amer. Math. Soc. 230 (1977), 1-40
MSC: Primary 22E43
MathSciNet review: 0453925
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Abstract: All the unitary equivalence classes of irreducible integrable and square-integrable representations of the groups $ {\text{Spin}}(1,2m),m \geqslant 2$, are determined. The method makes use of some elementary results on differential equations and the classification of irreducible unitary representations of these groups. In the latter classification, certain ambiguities resulting from possible equivalences not taken into account in a previous paper, are cleared up here.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0453925-7
Keywords: Discrete series of $ {\text{Spin}}\;(1,2m)$, discrete series of generalized Lorentz groups, unitary representations of rank 1 real semisimple Lie groups, unitary representations of $ {\text{Spin}}\;(1,2m)$, Eisenstein integrals of $ {\text{Spin}}(1,2m)$
Article copyright: © Copyright 1977 American Mathematical Society