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Lifting of generic depth zero representations of classical groups. (English) Zbl 1147.22008
In this paper the author considers split classical groups of type \(B\) and \(C\) over a \(p\)-adic field \(k\). It is now known that generic depth zero supercuspidal representations of these lift to representations of appropriate general linear groups. The author studies this correspondence in more detail. He considers the decomposition of induced representations of the type \(I(s,\Pi \times \Sigma)\) at \(s=1\) constructed on a larger group of the same family as the original one. Here \(\Pi\) is a depth zero self-dual supercuspidal representation of a general linear group over \(k\) and \(\Sigma\) is a depth zero generic supercuspidal representation of the original group which corresponds to a tame regular discrete series representation. He also considers the behaviour of the \(L\) and \(\epsilon\) functions involved.

22E35 Analysis on \(p\)-adic Lie groups
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