Modules over the small quantum group and semi-infinite flag manifold

We develop a theory of perverse sheaves on the semi-infinite flag manifold $G((t))/N((t))\cdot T[[t]]$, and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity

Some results about geometric Whittaker model

Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G and denote by U its unipotent radical. Let X be a G-variety. The purpose of this paper is to give two examples of a situation in which the functor of averaging of ℓ-adic sheaves on X with respect to a generic character commutes with Verdier duality. Namely, in the first example we take X to be an arbitrary G-variety and we prove the above property for all -equivariant sheaves on X where is the unipotent radical of an opposite parabolic subgroup; in the second example we take X=G and we prove the corresponding result for sheaves which are equivariant under the adjoint action (the latter result was conjectured by B. C. Ngo who proved it for G=GL(n)). As an application of the proof of the first statement we reprove a theorem of N. Katz and G. Laumon about local acyclicity of the kernel of the Fourier–Deligne transform

Neurophysiological Measures and Alcohol Use Disorder (AUD): Hypothesizing Links between Clinical Severity Index and Molecular Neurobiological Patterns

In 1987, Cloninger proposed a clinical description and classification of different personality traits genetically defined and independent from each other. Moreover, he elaborated a specific test the TCI to investigate these traits/states. The study of craving in Alcohol Use Disorder (AUD) assumed a greater significance, since ever more data seems to suggest a direct correlation between high levels of craving and a higher risk of relapse in alcoholics. Thus, our study aim is to explore the possible correlations among TCI linked molecular neurobiological pattern (s), craving and alcohol addiction severity measures in a sample of Italian alcoholics