scholarly journals An integral representation of an eigenfunction of invariant differential operators on a symmetric space

1974 ◽  
Vol 4 (2) ◽  
pp. 413-419 ◽  
Author(s):  
Toru Inoue ◽  
Kiyosato Okamoto ◽  
Makoto Tanaka
Keyword(s):  
Symmetric Space ◽  
Integral Representation ◽  
Differential Operators ◽  
Invariant Differential Operators ◽  
Invariant Differential

Eigenfunctions of Invariant Differential Operators on a Symmetric Space

1978 ◽  
Vol 107 (1) ◽  
pp. 1 ◽  
Author(s):  
M. Kashiwara ◽  
A. Kowata ◽  
K. Minemura ◽  
K. Okamoto ◽  
T. Oshima ◽  
...  
Keyword(s):  
Symmetric Space ◽  
Differential Operators ◽  
Invariant Differential Operators ◽  
Invariant Differential

scholarly journals Some results on Semisimple Symmetric Spaces and Invariant Differential Operators

2017 ◽  
Vol 116 (2) ◽  
Author(s):  
Trần Đạo Dõng
Keyword(s):  
Symmetric Space ◽  
Open Subset ◽  
Symmetric Spaces ◽  
Differential Operators ◽  
Analytic Manifold ◽  
Invariant Differential Operators ◽  
Semisimple Symmetric Space ◽  
Real Analytic Manifold ◽  
Invariant Differential ◽  
Real Analytic

<pre>Let X = G/H be a semisimple symmetric space of non-compact style. Our purpose is to construct a compact real analytic manifold in which the semisimple symmetric space X = G/H is realized as an open subset and that $G$ acts analytically on it.</pre><pre> By the <span>Cartan</span> decomposition <span>G = KAH,</span> we must <span>compacify</span> the <span>vectorial</span> part <span>A.$</span></pre><pre> In [6], by using the action of the Weyl group, we constructed a compact real analytic manifold in which the semisimple symmetric space G/H is realized as an open subset and that G acts analytically on it.</pre><pre>Our construction is a motivation of the <span>Oshima's</span> construction and it is similar to those in N. <span>Shimeno</span>, J. <span>Sekiguchi</span> for <span>semismple</span> symmetric spaces.</pre><pre>In this note, first we will <span>inllustrate</span> the construction via the case of <span>SL (n, </span>R)/SO_e (1, n-1) and then show that the system of invariant differential operators on X = G/H extends analytically on the corresponding compactification. </pre>

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