Whittaker supports for representations of reductive groups

Let $F$ be either $\mathbb{R}$ or a finite extension of $\mathbb{Q}_p$, and let $G$ be a finite central extension of the group of $F$-points of a reductive group defined over $F$. Also let $\pi$ be a smooth representation of $G$ (Frechet of moderate growth if $F=\mathbb{R}$). For each nilpotent orbit $\mathcal{O}$ we consider a certain Whittaker quotient $\pi_{\mathcal{O}}$ of $\pi$. We define the Whittaker support WS$(\pi)$ to be the set of maximal $\mathcal{O}$ among those for which $\pi_{\mathcal{O}}\neq 0$. In this paper we prove that all $\mathcal{O}\in\mathrm{WS}(\pi)$ are quasi-admissible nilpotent orbits, generalizing some of the results in [Moe96,JLS16]. If $F$ is $p$-adic and $\pi$ is quasi-cuspidal then we show that all $\mathcal{O}\in\mathrm{WS}(\pi)$ are $F$-distinguished, i.e. do not intersect the Lie algebra of any proper Levi subgroup of $G$ defined over $F$. We also give an adaptation of our argument to automorphic representations, generalizing some results from [GRS03,Shen16,JLS16,Cai] and confirming some conjectures from [Ginz06]. Our methods are a synergy of the methods of the above-mentioned papers, and of our preceding paper [GGS17]

Analytic continuation of equivariant distributions

We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein’s theory of analytic continuation of holonomic distributions. We use this to construct H-equivariant functionals on principal series representations of G, where G is a real reductive group and H is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on principal series representations and of analytic continuation of standard intertwining operators. Finally, we extend our constructions to the p-adic case using a recent result of Hong and Sun

Raising and Lowering Operators for Askey-Wilson Polynomials

In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra

With a Little Help From My Friends: Selective Social Potentiation of Emotion Regulation

Decades of research has pointed to emotion regulation (ER) as a critical ingredient for health, well-being, and social functioning. However, the vast majority of this research has examined ER in a social vacuum, despite the fact that in everyday life individuals frequently regulate their emotions with help from other people. The present collection of preregistered studies examined whether social help increases the efficacy of reappraisal, a widely studied ER strategy that involves changing how one thinks about emotional stimuli. In Study 1 (N = 40 friend pairs), we compared the efficacy of reinterpreting the content of negative stimuli alone (solo ER) to listening to a friend reinterpret the stimuli (social ER). We found that social ER was more effective than solo ER, and that the efficacy of these strategies was correlated within individuals. In Studies 2 and 3, we replicated effects from Study 1, and additionally tested alternate explanations for our findings. In Study 2 (N = 40 individuals), we failed to find evidence that social ER was more effective than solo ER due to a difference in the quality of reinterpretations, and in Study 3 (N = 40 friend pairs), we found that social help did not significantly attenuate negative affect in the absence of reappraisal. In sum, we found that social help selectively potentiates the efficacy of reappraisal, and that this effect was not merely the outcome of social buffering. Together, these results provide insight into how social relationships can directly lend a hand in implementing ER strategies. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

Bandes de « microbes » et insécurité à Abidjan

Le phénomène des gangs de « microbes » a tendance à s’étendre sur l’ensemble du territoire du district d’Abidjan, mais surtout à accroître le nombre des victimes. L’objectif de cette étude est de déterminer les actes criminels perpétrés par les « microbes » et de montrer comment ce phénomène est vécu au sein des populations. La méthodologie est basée sur une recherche documentaire et de terrain auprès des populations. L’analyse qualitative a permis de mettre en évidence la criminalité et le sentiment d’insécurité au sein de la population. Les résultats ont mis en exergue le fait que les multiples agressions des « microbes », à la fois violentes et récurrentes, ont conduit à de nombreux blessés voire décès des victimes. Aussi, ont-ils concouru à l’instauration d’un sentiment d’insécurité au sein des populations abidjanaise

Biorthogonal Expansion of Non-Symmetric Jack Functions

We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner-Pollaczek type polynomials. This is done by computing the Cherednik-Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function

Isolation and expression analysis of salt stress-associated ESTs from contrasting rice cultivars using a PCR-based subtraction method

Salt stress adversely affects the growth of rice plants. To understand the molecular basis of salt-stress response, four subtracted cDNA libraries were constructed employing specific NaCl-stressed tissues from salt-tolerant (CSR 27 and Pokkali) and salt-sensitive (Pusa basmati 1) rice cultivars. An efficient PCR-based cDNA subtraction method was employed for the isolation of the salt-stress responsive cDNA clones. In all, 1,266 cDNA clones were isolated in the course of this study, out of which 85 clones were end-sequenced. Database search of the sequenced clones showed that 22 clones were homologous to genes that have earlier been implicated in stress response, 34 clones were novel with respect to their function and six clones showed no homology to sequences in any of the public database. Northern analysis showed that the transcript expression pattern of selected clones was variable amongst the cultivars tested with respect to stress-regulation