I. Leonov,1 A. N. Yaresko,2 V. N. Antonov,3 and V. I. Anisimov4 1Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, Augsburg, Germany 2Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany 3Institute of Metal Physics, Vernadskii Street, 03142 Kiev, Ukraine 4Institute of Metal Physics, Russian Academy of S...

Preface 1 1. Classical groups 4 2. Parabolic induction 10 3. Admissible representations 16 4. Jacquet modules and cuspidal representations 24 5. Composition series of induced representations of SL(2, F ) and GL(2, F ) 34 6. Some examples 39 7. Parabolically induced representations of SL(2, F ) and GL(2, F ) 45 8. Some general consequences 52 9. GL(n, F ) 55 10. GSp(n, F ) 62 11. On the reducibi...

Let π $\pi$ be a cuspidal automorphic representation of GSp 4 ( A Q ) $\operatorname{GSp}_4(\mathbf {A}_\mathbf {Q})$ , whose archimedean component is holomorphic discrete series or limit representation. If not CAP endoscopic, then we show that its associated ℓ $\ell$ -adic Galois representations are irreducible and crystalline for 100 % $100\%$ primes . If, moreover, neither an induction nor s...

GSP's need their humans, and love them dearly. They are often referred to as "Velcro Dogs" because they can be very clingy. They are anxious to please and fond of children, though standoffish with strangers. They are also very intellegent dogs and many are "practical jokers". If they do not receive enough exercise, they can become destructive or nervous if neglected. If you are thinking about a...

A generic Lagrangian, in arbitrary spacetime dimension, describing the interaction of a graviton, a dilaton and two antisymmetric tensors is considered. An isotropic p-brane solution consisting of three blocks and depending on four parameters in the Lagrangian and two arbitrary harmonic functions is obtained. For speci c values of parameters in the Lagrangian the solution may be identi ed with ...

We prove uniqueness and give precise criteria for existence of split and non-split Bessel models for a class of lowest and highest weight representations of the groups GSp(4,R) and Sp(4,R) including all holomorphic and anti-holomorphic discrete series representations. Explicit formulas for the resulting Bessel functions are obtained by solving systems of differential equations. The formulas are...

Four groups of patients with social phobia (SP) were compared with regard to psychopathologic characteristics, personality traits, and social and occupational functioning. Fifteen persons with discrete social phobia without any personality disorder (DSP), 28 persons with generalized social phobia (GSP) without any personality disorder, 24 persons with GSP with a single diagnosis of avoidant per...

Methods of theta correspondence are used to analyze local and global Bessel models for GSp4 proving a conjecture of Gross and Prasad which describes these models in terms of local epsilon factors in the local case, and the nonvanishing of central critical L-value in the global case.