scholarly journals On Jacquet Modules of Induced Representations of p—Adic Symplectic Groups

Author(s):  
Marko Tadić
2003 ◽  
Vol 14 (05) ◽  
pp. 461-477
Author(s):  
Jian Zhou

We prove a double coset formula for induced representations of compact Lie groups. We apply it to the representation rings of unitary and symplectic groups to obtain Hopf algebras. We also construct a Heisenberg algebra representation based on the restiction and induction of representations of unitary groups.


2018 ◽  
Author(s):  
Joel Eduardo Martinez ◽  
Lauren Feldman ◽  
Mallory Feldman ◽  
Mina Cikara

Scholars from across the social and media sciences have issued a clarion call to address a recent resurgence in criminalized characterizations of immigrants. Do these characterizations meaningfully impact individuals’ beliefs about immigrants and immigration? Across two online convenience samples (N = 1,054 adult U.S. residents), we applied a novel analytic technique to test how different narratives—criminal, achievement, struggle-oriented—impact cognitive representations of German, Russian, Syrian, and Mexican immigrants and the concept of “immigrants” in general. All stories featured male targets. Achievement stories homogenized individual immigrant representations whereas both criminal and struggle-oriented stories racialized them along a white/non-white axis: Germany clustered with Russia, Syria with Mexico. However, criminal stories were unique in making our most egalitarian participants’ representations as differentiated as our least egalitarian participants’. Narratives about individual immigrants also generalized to update representations of nationality groups. Most important, narrative-induced representations correlated with immigration policy preferences: achievement narratives and corresponding homogenized representations promoted preferences for less restriction, criminal narratives for more.


Author(s):  
Fan Gao

Abstract For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for certain saturated covers of a semisimple simply connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.


2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu

We construct the $p$-adic standard $L$-functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to $p$-adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.


2021 ◽  
Vol 32 (2) ◽  
pp. 135-152
Author(s):  
Joel E. Martinez ◽  
Lauren A. Feldman ◽  
Mallory J. Feldman ◽  
Mina Cikara

Scholars from across the social and media sciences have issued a clarion call to address a recent resurgence in criminalized characterizations of immigrants. Do these characterizations meaningfully impact individuals’ beliefs about immigrants and immigration? Across two online convenience samples (total N = 1,054 adult U.S. residents), we applied a novel analytic technique to test how different narratives—achievement, criminal, and struggle-oriented—impacted cognitive representations of German, Russian, Syrian, and Mexican immigrants and the concept of immigrants in general. All stories featured male targets. Achievement stories homogenized individual immigrant representations, whereas both criminal and struggle-oriented stories racialized them along a White/non-White axis: Germany clustered with Russia, and Syria clustered with Mexico. However, criminal stories were unique in making our most egalitarian participants’ representations as differentiated as our least egalitarian participants’. Narratives about individual immigrants also generalized to update representations of nationality groups. Most important, narrative-induced representations correlated with immigration-policy preferences: Achievement narratives and corresponding homogenized representations promoted preferences for less restriction, and criminal narratives promoted preferences for more.


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