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via their restriction to compact open subgroups was begun by Mautner, Shalika and Tanaka for groups of type AI. In contrast to real reductive groups where the representation theory of a maximal compact subgroup K is given in terms of slight modifications to Cartan's theory of the highest weight, the representation theory of a (compact) parahoric subgroup ,~ is quite complicated. There is still no comprehensive theory for classifying the irreducible representa- tions. In the case of

Unrefined minimal K-types forp-adic groups