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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Boundary value maps, Szegö maps and intertwining operators

Author: L. Barchini
Journal: Trans. Amer. Math. Soc. 349 (1997), 1877-1900
MSC (1991): Primary 22C05, 22E45, 22E46
MathSciNet review: 1401761
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Abstract: We consider one series of unitarizable representations, the cohomological induced modules $A_{\mathfrak {q}}(\lambda )$ with dominant regular infinitesimal character. The minimal $K$-type $(\tau , V)$ of $A_{\mathfrak {q}}(\lambda )$ determines a homogeneous vector bundle $V_{\tau } \longrightarrow G/K $. The derived functor modules can be realized on the solution space of a first order differential operator $\mathcal {D}_{\mathfrak {l}}^{\lambda } $ on $V_{\tau }$. Barchini, Knapp and Zierau gave an explicit integral map $\mathcal {S}$ from the derived functor module, realized in the Langlands classification, into the space of smooth sections of the vector bundle $V_{\tau } \longrightarrow G/K $. In this paper we study the asymptotic behavior of elements in the image of $\mathcal {S}$. We obtain a factorization of the standard intertwining opeartors into the composition of the Szegö map $\mathcal {S}$ and a passage to boundary values.

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Additional Information

L. Barchini
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Address at time of publication: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078

Received by editor(s): February 17, 1995
Received by editor(s) in revised form: October 9, 1995
Article copyright: © Copyright 1997 American Mathematical Society