Skip to main content Accessibility help


  • IVAN MATIĆ (a1)


We study induced representations of the form $\unicode[STIX]{x1D6FF}_{1}\times \unicode[STIX]{x1D6FF}_{2}\rtimes \unicode[STIX]{x1D70E}$ , where $\unicode[STIX]{x1D6FF}_{1},\unicode[STIX]{x1D6FF}_{2}$ are irreducible essentially square-integrable representations of general linear group and $\unicode[STIX]{x1D70E}$ is a strongly positive discrete series of classical $p$ -adic group, which naturally appear in the nonunitary dual. For $\unicode[STIX]{x1D6FF}_{1}=\unicode[STIX]{x1D6FF}([\unicode[STIX]{x1D708}^{a}\unicode[STIX]{x1D70C}_{1},\unicode[STIX]{x1D708}^{b}\unicode[STIX]{x1D70C}_{1}])$ and $\unicode[STIX]{x1D6FF}_{2}=\unicode[STIX]{x1D6FF}([\unicode[STIX]{x1D708}^{c}\unicode[STIX]{x1D70C}_{2},\unicode[STIX]{x1D708}^{d}\unicode[STIX]{x1D70C}_{2}])$ with $a\geqslant 1$ and $c\geqslant 1$ , we determine composition factors of such induced representation.



Hide All
[1] Arthur, J., “ The endoscopic classification of representations. Orthogonal and symplectic groups ”, American Mathematical Society Colloquium Publications 61 , American Mathematical Society, Providence, RI, 2013.
[2] Bernstein, I. N. and Zelevinsky, A. V., Induced representations of reductive p-adic groups. I , Ann. Sci. Éc. Norm. Supér. (4) 10 (1977), 441472.
[3] Jantzen, C., On supports of induced representations for symplectic and odd-orthogonal groups , Amer. J. Math. 119 (1997), 12131262.
[4] Matić, I., Strongly positive representations of metaplectic groups , J. Algebra 334 (2011), 255274.
[5] Matić, I., Theta lifts of strongly positive discrete series: the case of (˜Sp (n), O (V)) , Pacific J. Math. 259 (2012), 445471.
[6] Matić, I., Jacquet modules of strongly positive representations of the metaplectic group ˜Sp (n) , Trans. Amer. Math. Soc. 365 (2013), 27552778.
[7] Matić, I., Strongly positive subquotients in a class of induced representations of classical p-adic groups , J. Algebra 444 (2015), 504526.
[8] Matić, I., On Jacquet modules of discrete series: the first inductive step , J. Lie Theory 26 (2016), 135168.
[9] Matić, I., On discrete series subrepresentations of the generalized principal series , Glas. Mat. Ser. III 51(71) (2016), 125152.
[10] Matić, I. and Tadić, M., On Jacquet modules of representations of segment type , Manuscripta Math. 147 (2015), 437476.
[11] Mœglin, C., “ Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands ”, in Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski-Shapiro, Contemp. Math. 614 , Amer. Math. Soc., Providence, RI, 2014, 295336.
[12] Mœglin, C. and Tadić, M., Construction of discrete series for classical p-adic groups , J. Amer. Math. Soc. 15 (2002), 715786.
[13] Muić, G., Composition series of generalized principal series; the case of strongly positive discrete series , Israel J. Math. 140 (2004), 157202.
[14] Tadić, M., Representations of p-adic symplectic groups , Compos. Math. 90 (1994), 123181.
[15] Tadić, M., Structure arising from induction and Jacquet modules of representations of classical p-adic groups , J. Algebra 177 (1995), 133.
[16] Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques (d’après Harish-Chandra) , J. Inst. Math. Jussieu 2 (2003), 235333.
[17] Zelevinsky, A. V., Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n) , Ann. Sci. Éc. Norm. Supér. (4) 13 (1980), 165210.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed