Matrix coefficients of cohomologically induced representations

AbstractLet{G^{1}}be an orthogonal, symplectic or unitary group over a local field and let{P=MN}be a maximal parabolic subgroup. Then the Levi subgroupMis the product of a group of the same type as{G^{1}}and a general linear group, acting on vector spacesXandW, respectively. In this paper we decompose the unipotent radicalNofPunder the adjoint action ofM, assuming{\dim W\leq\dim X}, excluding only the symplectic case with{\dim W}odd. The result is a Weyl-type integration formula forNwith applications to the theory of intertwining operators for parabolically induced representations of{G^{1}}. Namely, one obtains a bilinear pairing on matrix coefficients, in the spirit of Goldberg–Shahidi, which detects the presence of poles of these operators at 0.

Download Full-text

Narratives shape cognitive representations of immigrants and policy preferences

10.31234/osf.io/d9hrj ◽

2018 ◽

Cited By ~ 2

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.

Download Full-text

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

Forum Mathematicum ◽

10.1515/forum-2020-0054 ◽

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.

Download Full-text

Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

Advances in Difference Equations ◽

10.1186/s13662-021-03427-4 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Adisorn Kittisopaporn ◽

Pattrawut Chansangiam

Keyword(s):

Least Squares ◽

Iterative Algorithm ◽

Gradient Descent ◽

Main Idea ◽

Full Column Rank ◽

Minimum Error ◽

Matrix Coefficients ◽

Special Cases ◽

Efficiency And Effectiveness ◽

Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

Download Full-text

Narratives Shape Cognitive Representations of Immigrants and Immigration-Policy Preferences

Psychological Science ◽

10.1177/0956797620963610 ◽

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.

Download Full-text

General finite-volume framework for saddle-point problems of various physics

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2021-0029 ◽

2021 ◽

Vol 36 (6) ◽

pp. 359-379

Author(s):

Kirill M. Terekhov

Keyword(s):

Saddle Point ◽

Finite Volume ◽

Navier Stokes ◽

Saddle Point Problems ◽

Surface Integral ◽

Matrix Coefficients ◽

Gauss Theorem ◽

Stability Issue ◽

Incompressible Elasticity ◽

Vector Flux

Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

Download Full-text