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The explicit Zelevinsky–Aubert duality
- Part of
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- Journal:
- Compositio Mathematica / Volume 159 / Issue 2 / February 2023
- Published online by Cambridge University Press:
- 20 February 2023, pp. 380-418
- Print publication:
- February 2023
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- Article
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In this paper, we give an explicit computable algorithm for the Zelevinsky–Aubert duals of irreducible representations of
$p$-adic symplectic and odd special orthogonal groups. To do this, we establish explicit formulas for certain derivatives and socles. We also give a combinatorial criterion for the irreducibility of certain parabolically induced representations.
