On the Jacquet Conjecture on the Local Converse Problem for p-adic GLn
Abstract
Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GLN that have the same depth and central character admit a special pair of Whittaker functions. This result gives a new reduction towards a final proof of Jacquet's conjecture on the local converse problem for GLN. As a corollary of our result, we prove Jacquet's conjecture for GLN, when N is prime.
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