In this paper we begin to explore the relation between the question of unitarizability of classical
p
-adic groups, and Arthur packets, starting from Tadić (Mem Am Math Soc 2020, to appear).
Given a (complex, smooth) irreducible representation $\pi$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $\sigma$ of a classical ...group, we show that the (normalized) parabolic induction $\pi\rtimes\sigma$ is reducible if there exists $\rho$ in the supercuspidal support of $\pi$ such that $\rho\rtimes\sigma$ is reducible. In special cases we also give irreducibility criteria for $\pi\rtimes\sigma$ when the above condition is not satisfied.
Natural language processing for languages with limited resources is hampered by a lack of data. Using English as a hub language for such languages, cross-lingual sentiment analysis has been ...developed. The sheer quantity of English language resources raises questions about its status as the primary resource. This research aims to examine the impact on sentiment analysis of adding data from same-family versus distant-family languages. We analyze the performance using low-resource and high-resource data from the same language family (Slavic), investigate the effect of using a distant-family language (English) and report the results for both settings. Quantitative experiments using multi-task learning demonstrate that adding a large quantity of data from related and distant-family languages is advantageous for cross-lingual sentiment transfer.
Let
G
n
denote either the group
Sp
(
n
,
F
) or
SO
(2
n
+ 1,
F
) over a local non-archimedean field
F
. We study representations of segment type of group
G
n
, which play a fundamental role in the ...constructions of discrete series, and obtain a complete description of the Jacquet modules of these representations. Also, we provide an alternative way for determination of Jacquet modules of strongly positive discrete series and a description of top Jacquet modules of general discrete series.
To an irreducible square integrable representation
π
of a classical
p
-adic group, Mœglin has attached invariants Jord(
π
),
π
cusp
and
. These triples classify square integrable representations ...modulo cuspidal data (assuming a natural hypothesis). The definition of these invariants in Mœglin (J Eur Math Soc 4(2):143–200,
2002
) is rather simple—in terms of induced representations, except at one case when a coherent normalization of standard intertwining operators is required. In this paper we show how one can define this case also in terms of induced representations.
The aim of this paper is to prove two general results on parabolic induction of classical
$p$
-adic groups (actually, one of them holds also in the archimedean case), and to obtain from them some ...consequences about irreducible unitarizable representations. One of these consequences is a reduction of the unitarizability problem for these groups. This reduction is similar to the reduction of the unitarizability problem to the case of real infinitesimal character for real reductive groups.
This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square ...integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.
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