20,692 research outputs found
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 be a connected real reductive group with maximal compact subgroup
of equal rank, and let be the category of Harish-Chandra modules
for . We relate three differentely defined pairings between two finite
length modules and in : the Euler-Poincar\'e pairing, the
natural pairing between the Dirac indices of and , and the elliptic
pairing. (The Dirac index is a virtual finite dimensional representation of
, the spin double cover of .) 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 for any finite length Harish-Chandra module . These
functions are very cuspidal in the sense of Labesse, and their orbital
integrals on elliptic elements coincide with the character of . 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 -adic
groups.Comment: 25 page
CSM analyses of
We study the modifications of the amplitudes and cross sections of several
processes, especially , 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
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