From Twisted Quantum Loop Algebras to Twisted Yangians

We prove how the Yangian of $\mathfrak{gl}_N$ in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues

Vertex Representations for Yangians of Kac-Moody algebras

30 pagesUsing vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.Peer reviewe

Representations of twisted Yangians of types B, C, D: II

We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs $(\mathfrak{so}_N,\mathfrak{so}_{N-2} \oplus \mathfrak{so}_2)$ and $(\mathfrak{so}_{2n+1},\mathfrak{so}_{2n})$

Quantized enveloping superalgebra of type PP

We introduce a new quantized enveloping superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ attached to the Lie superalgebra ${\mathfrak{p}}_n$ of type $P$. The superalgebra $\mathfrak{U}_q{\mathfrak{p}}_n$ is a quantization of a Lie bisuperalgebra structure on ${\mathfrak{p}}_n$ and we study some of its basic properties. We also introduce the periplectic $q$-Brauer algebra and prove that it is the centralizer of the $\mathfrak{U}_q {\mathfrak{p}}_n$-module structure on ${\mathbb C}(n|n)^{\otimes l}$. We end by proposing a definition for a new periplectic $q$-Schur superalgebra.Comment: 14 page

The role of genetic selection on agonistic behavior and welfare of gestating sows housed in large semi-static groups

Confinement of gestating sows is becoming banished in favor of group-housing in countries worldwide, forcing breeding companies to develop genetic lines adapted for social living. This study aimed at assessing the influence of two genetic lines selected for high performance (HP1, HP2, derived from Landrace × Yorkshire) on welfare and reproductive performance of sows housed in large semi-static groups (20 groups of 46–91 animals) across several parities. To address this, agonistic behaviors were recorded on d0, d2, d27, and d29 post-mixing while body lesions were scored on d1, d26, and d84. Sows’ individual and reproductive performances were also recorded. HP2 sows were more aggressive than HP1 sows since they fought (p = 0.028) and bullied (p = 0.0009) pen-mates more frequently on d0–d2. HP2 sows had more total body lesions throughout gestation than HP1 sows at higher parities (p < 0.0001). Regarding reproductive performance, HP2 sows lost less piglets (p < 0.0001) and tended to wean more piglets (p = 0.067) than HP1 sows. In conclusion, while HP2 sows were the most aggressive, HP1 sows had piglets with lower survivability, which raises ethical issues in both cases and points to the need of considering social aspects when developing genetic lines for group-housing

On the category O for rational Cherednik algebras

We study the category O of representations of the rational Cherednik algebra A attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov functor, from O to the category of H-modules, where H is the (finite) Iwahori-Hecke algebra associated to W. We prove that the Knizhnik-Zamolodchikov functor induces an equivalence between O/O_tor, the quotient of O by the subcategory of A-modules supported on the discriminant and the category of finite-dimensional H-modules. The standard A-modules go, under this equivalence, to certain modules arising in Kazhdan-Lusztig theory of ``cells'', provided W is a Weyl group and the Hecke algebra H has equal parameters. We prove that the category O is equivalent to the module category over a finite dimensional algebra, a generalized "q-Schur algebra" associated to W.Comment: 28 pp., LaTeX, final version, to appear in Invent. Mat

Idéations suicidaires du personnel de la santé pendant la pandémie de COVID-19 : une évaluation écologique momentanée

Introduction: The COVID-19 pandemic had an impact on the psychological health of healthcare workers (HCWs). Cross-sectional studies report suicidal ideation in this population during this period, but no longitudinal study has examined the evolution of these ideas over time. Objectives: To assess the evolution of suicidal ideation of HCWs during the first two waves of the COVID-19 pandemic among Quebec (Canada) HCWs and to identify the risk factors involved. Methods: A longitudinal study among Quebec (Canada) HCWs using ecological momentary assessment was conducted between May 8, 2020, and March 31, 2021 (corresponding to the second half of the first wave to the end of the second). Participants (n=865) answered weekly questions related to anxiety (GAD-7), depression (PHQ-9), suicidal ideation (PHQ-9 Q.9), exposure to COVID-19, exposure to COVID-19-related deaths, their infection status and that of their co-workers and loved ones, as well as the amount of time they spent consuming news related to COVID-19. Results: Proportion of suicidal ideation increased from May to June 2020 (second half of the first wave) peaking at 18% before declining up to March 2021. Anxiety and depression symptoms severity increased those ideations as well as having a colleague confirmed positive to COVID-19. Social support does not appear to be a protective factor for suicidal ideation. Suicidal thoughts are associated with media consumption and appear to be mediated by the presence of clinical distress expressed as depressive or anxiety states. Discussion and conclusion: Media consumption in a pandemic context is associated with anxiety and depression, the more severe states of which may express suicidal ideation. Without inferring causality relationship, it seems advisable for HCWs to limit their media exposure during a disaster such as a pandemic.Introduction : La pandémie de COVID-19 a eu un impact sur la santé psychologique des travailleurs de la santé (TS). Des études transversales rapportent la présence d’idées suicidaires chez cette population pendant cette période, mais aucune étude longitudinale n’a examiné l’évolution de ces idées dans le temps. Objectifs : Évaluer l’évolution des idées suicidaires des TS au cours des deux premières vagues de la pandémie de COVID-19 au Québec (Canada) et identifier les facteurs de risque impliqués. Méthodes&nbsp;: Une étude longitudinale, utilisant l’évaluation écologique momentanée, a été menée entre le 8 mai 2020 et le 31 mars 2021 (correspondant à la période entre la moitié de la 1re vague à la fin de la seconde) auprès des TS québécois. Les participants (n=865) ont répondu de façon hebdomadaire à des questions relatives à l’anxiété (GAD-7), à la dépression (PHQ-9), aux idées suicidaires (PHQ-9 Q.9), à l’exposition à la COVID-19, à l’exposition aux décès liés à la COVID-19, à leur statut infectieux et à celui de leurs collègues et de leurs proches, ainsi qu’au temps passé à consommer des nouvelles liées à la COVID-19. Résultats : La proportion d’idées suicidaires a augmenté de mai à juin 2020 (deuxième moitié de la première vague) atteignant un pic à 18% avant de diminuer par la suite jusqu’en mars 2021. La gravité des symptômes d’anxiété et de dépression était corrélée positivement avec les idéations suicidaires, tout comme le fait d’avoir un collègue infecté à la COVID-19. Le soutien social ne semble pas être un facteur protecteur des idées suicidaires. Les idées suicidaires sont corrélées à la consommation de médias et un effet médiateur est observé par la présence d’une détresse clinique exprimée par des états dépressifs ou anxieux. Discussion et conclusion : La consommation de médias dans un contexte de pandémie est associée à de l’anxiété et à de la dépression, dont les états les plus graves peuvent exprimer des idées suicidaires. Sans inférer un lien de causalité, il semble recommandé aux travailleurs de la santé de limiter leur exposition aux médias lors d’une catastrophe telle qu’une pandémie