Glasnik Matematicki, Vol. 51, No. 1 (2016), 125152.
ON DISCRETE SERIES SUBREPRESENTATIONS OF THE GENERALIZED PRINCIPAL SERIES
Ivan Matić
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia
email: imatic@mathos.hr
Abstract.
We study a family of the generalized principal series and obtain necessary and sufficient conditions under which the induced representation of studied form contains a discrete series subquotient. Furthermore, we show that if the generalized principal series which belongs to the studied family has a discrete series subquotient, then it has a discrete series subrepresentation.
2010 Mathematics Subject Classification.
22E35, 22E50, 11F70.
Key words and phrases. Discrete series, classical padic groups, Jacquet modules.
Full text (PDF) (access from subscribing institutions only)
DOI: 10.3336/gm.51.1.08
References:

J. Arthur, The endoscopic classification of representations. Orthogonal and symplectic groups,
American
Mathematical Society, Providence, 2013.
MathSciNet

I. N. Bernstein and A. V. Zelevinsky, Induced representations of
reductive padic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977),
441472.
MathSciNet
link

M. Hanzer, The generalized injectivity conjecture for classical
padic groups, Int. Math. Res. Not. IMRN (2010), 2010, 195237.
MathSciNet
CrossRef

I. Matić, Strongly positive representations of metaplectic
groups, J. Algebra 334 (2011), 255274.
MathSciNet
CrossRef

I. Matić, The conservation
relation for discrete series representations of metaplectic groups, Int.
Math. Res. Not. IMRN (2013), 2013, 52275269.
MathSciNet

I. Matić, Jacquet modules of
strongly positive representations of the metaplectic group
Sp(n), Trans. Amer. Math. Soc. 365 (2013), 27552778.
MathSciNet
CrossRef

I. Matić, On Jacquet modules
of discrete series: the first inductive step, J. Lie Theory 26 (2016), 135168.
MathSciNet

I. Matić and M. Tadić, On Jacquet modules of
representations of segment type, Manuscripta Math. 147 (2015),
437476.
MathSciNet
CrossRef

C. Mœglin, Sur la classification des séries discrètes des
groupes classiques padiques: paramètres de Langlands et
exhaustivité, J. Eur. Math. Soc. (JEMS) 4 (2002), 143200.
MathSciNet
CrossRef

C. Mœglin and M. Tadić, Construction of discrete series for
classical padic groups, J. Amer. Math. Soc. 15 (2002), 715786.
MathSciNet
CrossRef

G. Muić, Composition series of generalized principal series; the
case of strongly positive discrete series, Israel J. Math. 140 (2004),
157202.
MathSciNet
CrossRef

G. Muić, Howe correspondence
for discrete series representations; the case of (Sp(n),O(V)), J.
Reine Angew. Math. 567 (2004), 99150.
MathSciNet
CrossRef

G. Muić, Reducibility of
generalized principal series, Canad. J. Math. 57 (2005), 616647.
MathSciNet
CrossRef

F. Shahidi, A proof of Langlands' conjecture on Plancherel
measures; complementary series for padic groups, Ann. of Math. (2) 132
(1990), 273330.
MathSciNet
CrossRef

F. Shahidi, Twisted endoscopy
and reducibility of induced representations for padic groups, Duke
Math. J. 66 (1992), 141.
MathSciNet
CrossRef

M. Tadić, Structure arising from induction and Jacquet modules
of representations of classical padic groups, J. Algebra 177 (1995),
133.
MathSciNet
CrossRef

M. Tadić, On tempered and
square integrable representations of classical padic groups, Sci. China
Math. 56 (2013), 22732313.
MathSciNet
CrossRef

A. V. Zelevinsky, Induced representations of reductive padic
groups. II. On irreducible representations of GL(n), Ann. Sci.
École Norm. Sup. (4) 13 (1980), 165210.
MathSciNet
link
Glasnik Matematicki Home Page