Returnees in the Maghreb. A European perspective. Egmont Security Policy Brief No. 120 December 2019

More than 10,000 individuals travelled from Europe and North Africa to fight in Syria and Iraq. Now, Europe and North Africa are dealing with the challenge of returning foreign fighters, mostly separately. This policy brief looks at the inter-regional dimension of the returnees’ challenge, at why Europe should care more about North Africa’s ability (or not) to craft effective policies, and how it could help – with a focus on the European Union (EU). It concludes with concrete recommendations for the EU and North African countries

Euler-Poincar\'e pairing, Dirac index and elliptic pairing for Harish-Chandra modules

Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of equal rank, and let $\mathscr M$ be the category of Harish-Chandra modules for $G$. We relate three differentely defined pairings between two finite length modules $X$ and $Y$ in $\mathscr M$ : the Euler-Poincar\'e pairing, the natural pairing between the Dirac indices of $X$ and $Y$, and the elliptic pairing. (The Dirac index is a virtual finite dimensional representation of $\widetilde K$, the spin double cover of $K$.) Analogy with the case of Hecke algebras and a formal (but not rigorous) computation lead us to conjecture that the first two pairings coincide. In the second part of the paper, we show that they are both computed as the indices of Fredholm pairs (defined here in an algebraic sense) of operators acting on the same spaces. We construct index functions $f_X$ for any finite length Harish-Chandra module $X$. These functions are very cuspidal in the sense of Labesse, and their orbital integrals on elliptic elements coincide with the character of $X$. From this we deduce that the Dirac index pairing coincide with the elliptic pairing. These results are the archimedean analog of results of Schneider-Stuhler for $p$-adic groups.Comment: 25 page

CSM analyses of e+e−→ttˉH,ttˉZ,tbˉWe^+e^- \to t\bar t H, t\bar t Z, t\bar b W

We study the modifications of the amplitudes and cross sections of several processes, especially $e^+e^- \to t\bar t H, t\bar t Z, t\bar b W$, generated by Higgs boson and top quark compositeness, in particular within the CSM concept. We illustrate the observable differences that may appear between various, CSM conserving or CSM violating, compositeness possibilities.Comment: 13 pages, 4 figure