Geodesic
The Topology of the Spectrum for Gelfand Pairs on Lie Groups
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 569-579

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Zbl MR
Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable subset of $\mathbb{C}^n$ and we prove the equivalence between Gelfand topology and euclidean topology. 
Ferrari Ruffino, Fabio. The Topology of the Spectrum for Gelfand Pairs on Lie Groups. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 569-579. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a5/
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     title = {The {Topology} of the {Spectrum} for {Gelfand} {Pairs} on {Lie} {Groups}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {569--579},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     zbl = {1182.43012 1177.22004},
     mrnumber = {2351529},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a5/}
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