Abstract
We have determined composition series of a class of induced representations appearing in Mœglin–Tadić classification of discrete series. The result is further used to determine the composition series of certain representations induced from Langlands quotients. This should provide more information on decomposing standard representations as well as Jacquet modules of discrete series, which has applications in automorphic forms.
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References
Bernstein, I.N., Zelevinsky, A.V.: Induced representations of reductive \(p\)-adic groups I. Ann. Sci. École Norm. Sup. (4) 10(4), 441–472 (1977)
Ciganović, I.: Composition series of a class of induced representations, a case of one half cuspidal reducibility. Pac. J. Math. 296(1), 21–30 (2018)
Matić, I.: First occurrence indices of tempered representations of metaplectic groups. Proc. Am. Math. Soc. 144(7), 3157–3172 (2016)
Matić, I.: Jacquet modules of strongly positive representations of the metaplectic group \(\widetilde{Sp(n)}\). Trans. Am. Math. Soc. 365(5), 2755–2778 (2013)
Mœglin, C.: Sur la classification des séries discrètes des groupes classiques \(p\)-adiques: paramètres de Langlands et exhaustivité. (French) [On the classification of discrete series of classical p-adic groups: Langlands parameters and completeness]. J. Eur. Math. Soc. (JEMS) 4(2), 143–200 (2002)
Mœglin, C., Tadić, M.: Construction of discrete series for classical \(p\)-adic groups. J. Am. Math. Soc. 15(3), 715–786 (2002)
Muić, G.: Composition series of generalized principal series; the case of strongly positive discrete series. Israel J. Math. 140, 157–202 (2004)
Muić, G.: Reducibility of generalized principal series. Can. J. Math. 57(3), 616–647 (2005)
Tadić, M.: Structure arising from induction and Jacquet modules of representations of classical \(p\)-adic groups. J. Algebra 177(1), 1–33 (1995)
Tadić, M.: A family of square integrable representations of classical \(p\)-adic groups in the case of general half-integral reducibilities Glas. Mat. Ser. III 37(1), 21–57 (2002)
Tadić, M.: On tempered and square integrable representations of classical p-adic groups. Sci. China Math. 56(11), 2273–2313 (2013)
Zelevinsky, A.V.: Induced representations of reductive \(p\)-adic groups. II. On irreducible representations of \(GL(n)\). Ann. Sci. École Norm. Sup. (4) 13(2), 165–210 (1980)
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The author is employed at Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10 000 Zagreb, Croatia.
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This work has been fully supported by Croatian Science Foundation under the project IP-2018-01-3628.
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Ciganović, I. Composition series of a class of induced representations built on discrete series. manuscripta math. 170, 1–18 (2023). https://doi.org/10.1007/s00229-021-01348-w
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DOI: https://doi.org/10.1007/s00229-021-01348-w