Abstract
Let F be a non-Archimedean local field, A be a central simple F-algebra, and G be the multiplicative group of A. It is known that for every irreducible supercuspidal representation π, there exists a [G,π]G-type (J,λ), called a (maximal) simple type. We will show that [G,π]G-types defined over some maximal compact subgroup are unique up to G-conjugations under some unramifiedness assumption on a simple stratum.
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