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By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation (Formula presented.) of a classical group (which may be not-quasi-split) over a non-archimedean local field of odd residual characteristic. From this, we can explicitly describe all the irreducible cuspidal representations in the union of one, two, or four (Formula presented.) -packets, containing (Formula presented.). These results generalize the work of DeBacker–Reeder (in the case of classical groups) from regular to arbitrary tame Langlands parameters.
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