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

1991 ◽  
pp. 305-314 ◽  
Author(s):  
Marko Tadić
Keyword(s):  
Symplectic Groups ◽  
Induced Representations

Representation Rings of Classical Groups and Hopf Algebras

2003 ◽  
Vol 14 (05) ◽  
pp. 461-477
Author(s):  
Jian Zhou
Keyword(s):  
Lie Groups ◽  
Hopf Algebras ◽  
Double Coset ◽  
Heisenberg Algebra ◽  
Unitary Groups ◽  
Symplectic Groups ◽  
Compact Lie Groups ◽  
Induced Representations ◽  
Algebra Representation ◽  
Representation Rings

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.

Narratives shape cognitive representations of immigrants and policy preferences

2018 ◽  
Author(s):  
Joel Eduardo Martinez ◽  
Lauren Feldman ◽  
Mallory Feldman ◽  
Mina Cikara
Keyword(s):  
Immigration Policy ◽  
Mexican Immigrants ◽  
Policy Preferences ◽  
Cognitive Representations ◽  
Induced Representations ◽  
The Social

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.

scholarly journals R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

2021 ◽  
pp. 1-61
Author(s):  
Fan Gao
Keyword(s):  
Series Representation ◽  
Principal Series ◽  
Symplectic Groups ◽  
Principal Series Representation ◽  
Connected Group ◽  
Covering Group ◽  
Simply Connected

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.

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

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.

-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu
Keyword(s):  
Eisenstein Series ◽  
Symplectic Group ◽  
Symplectic Groups ◽  
Simple Strategy ◽  
Doubling Method

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 $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.

scholarly journals Quadratic residue codes and symplectic groups

1974 ◽  
Vol 29 (1) ◽  
pp. 150-171 ◽  
Author(s):  
Harold N Ward
Keyword(s):  
Quadratic Residue ◽  
Symplectic Groups ◽  
Quadratic Residue Codes

scholarly journals Narratives Shape Cognitive Representations of Immigrants and Immigration-Policy Preferences

2021 ◽  
Vol 32 (2) ◽  
pp. 135-152
Author(s):  
Joel E. Martinez ◽  
Lauren A. Feldman ◽  
Mallory J. Feldman ◽  
Mina Cikara
Keyword(s):  
Immigration Policy ◽  
Mexican Immigrants ◽  
Policy Preferences ◽  
Cognitive Representations ◽  
Total N ◽  
Induced Representations ◽  
The Social

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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