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The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems

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Volume of a double class of a parahoric subgroup

Since you are posing the question for reductive $G$, you should work with the Iwahori Weyl group $W_{I}$ as this is what parametrizes $I\backslash G/ I$. However since the question is only about volum …
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