Computational analysis reveals symmetry in A-parameters of tempered and nontempered representations in odd orthogonal groups, suggesting deeper ties among them.
For a generic irreducible representation of the odd orthogonal group SO(2n + 1, F ) over a p -adic field F , we compute the Aubert involution and the corresponding L-parameter.We show that, among generic representations, only tempered representations are base points attached to A-parameters and prove that in this case the A -parameters of and are symmetric.In addition, we consider A-parameters of SO(2n + 1, F ) corresponding to certain nontempered representations and prove that and are symmetric.
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D. Ban (2006) studied this question.
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