I am looking for references for the Bernstein-Zelevisnky classification of irreducible representations of GL$(n,F)$ in terms of cuspidal representations. In particular I would like to find something different with respect to the article of the 1980 in which they explain it. Online there are few notes that speak about the classification but I didn't find anything with proofs.
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$\begingroup$ Are you looking for references other than Zelevinsky's original paper Induced representations of reductive $\mathfrak p$-adic groups. II. On irreducible representations of $\mathrm{GL}(n)$? $\endgroup$– Kenta SuzukiCommented Aug 30 at 19:38
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$\begingroup$ @KentaSuzuki Yes, I would like to find something else. $\endgroup$– MarioCommented Aug 31 at 7:38
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$\begingroup$ What is wrong about the original reference? $\endgroup$– Kenta SuzukiCommented Aug 31 at 14:15
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$\begingroup$ There isn’t any problem with the original reference, but I think to have other references can be useful. $\endgroup$– MarioCommented Sep 1 at 9:31
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There is an extension of this result which includes torsion coefficients (coprime to the residue characteristic of $F$) by Mínguez-Sécherre: Représentations lisses modulo $\ell$ de $\mathrm{GL}_n(D)$
Don't let the title confuse you, it also works in characteristic 0, also it is a purely algebraic proof, you find a discussion in the introduction of the paper.
