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Transactions of the American Mathematical Society

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Intertwining differential operators for $ {\rm Mp}(n,\,{\bf R})$ and $ {\rm SU}(n,\,n)$

Author: Hans Plesner Jakobsen
Journal: Trans. Amer. Math. Soc. 246 (1978), 311-337
MSC: Primary 22E45; Secondary 35L99, 47A15
MathSciNet review: 515541
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Abstract: For each of the two series of groups, three series of representations $ {U_n}$, $ {D_n}$, and $ {H_n}(n \in Z)$ are considered. For each series of representations there is a differential operator with the property, that raised to the nth power $ (n > 0)$, it intertwines the representations indexed by $ - n$ and n. The operators are generalizations of the d'Alembertian, the Diracoperator and a combination of the two. Unitarity of subquotients of representations indexed by negative integers is derived from the intertwining relations.

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Keywords: Representation, holomorphic function, upper half-plane, reproducing kernel, intertwining differential operator, subquotient, unitarity
Article copyright: © Copyright 1978 American Mathematical Society