Some results on reducibility of parabolic induction for classical groups

Given a (complex, smooth) irreducible representation $\pi$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $\sigma$ of a classical group, we show that the (normalized) parabolic induction $\pi\rtimes\sigma$ is reducible if there exists $\rho$ in the supercuspidal support of $\pi$ such that $\rho\rtimes\sigma$ is reducible. In special cases we also give irreducibility criteria for $\pi\rtimes\sigma$ when the above condition is not satisfied

A family of square integrable representations of classical p-adic groups in the case of general half-integral reducibilities

The main aim of this paper is a presentation of a large family of non-cuspidal irreducuble square integrable representations δ(Δ1, ... , Δk, σ)τ of symplectic and odd-orthogonal p-adic groups, starting from the cuspidal representations of the Levi subgroups. The only information that we need about these irreducible cuspidal representations are the generalized rank one reducibilities. We also get a number of interesting fact about these square integrable representations. In C. Moeglin and M. Tadic\u27s paper "Construction of discrete series for classical p-adic groups" (J. Amer. Math. Soc. 15 (2002), 715-786) is given a general construction of all the irreducible square integrable representations of the classical p-adic groups modulo cuspidal data (under a natural assumption). The construczion of the family that we present in this paper preceded the general construction. Although the general construction gives a construction of all the square integrable representations of classical p-adic groups, it is interesting to have also available this former construction. Namely, the construction that we preset here is much more direct than the general construction, and it gives a number of explicit information about representations. These facts may be useful in further study of the representations of the family that we construct in this paper. It is for expecting that we shall deal a lot in future with the representations of this family, since this family includes all the generic irreducible square integrable representations (for example). From Shahidi\u27s conjecture on exsistence of a generic representation in each L2 L-packet, would follow that each L2 L-packet contains some of the representation from the family whose construction we present in this paper

Sastavljanje Hrvatske ovisnosne banke stabala: početne etape

The paper presents work–in–progress on the building of the Croatian Dependency Treebank. Its design principles, procedures and the pilot corpus used within are described. Perspectives for further development of the Croatian Dependency Treebank are presented at the end.Članak donosi međurezultate sastavljanja Hrvatske ovisnosne banke stabala koje je istraživanje u tijeku. Opisuju se njezina načela oblikovanja, postupci i uporabljeni pilot korpus. Na kraju se članka predstavljaju perspektive za daljnji razvitak Hrvatske ovisnosne banke stabala

A family of square integrable representations of classical p-adic groups in the case of general half-integral reducibilities

The main aim of this paper is a presentation of a large family of non-cuspidal irreducuble square integrable representations δ(Δ1, ... , Δk, σ)τ of symplectic and odd-orthogonal p-adic groups, starting from the cuspidal representations of the Levi subgroups. The only information that we need about these irreducible cuspidal representations are the generalized rank one reducibilities. We also get a number of interesting fact about these square integrable representations. In C. Moeglin and M. Tadic\u27s paper "Construction of discrete series for classical p-adic groups" (J. Amer. Math. Soc. 15 (2002), 715-786) is given a general construction of all the irreducible square integrable representations of the classical p-adic groups modulo cuspidal data (under a natural assumption). The construczion of the family that we present in this paper preceded the general construction. Although the general construction gives a construction of all the square integrable representations of classical p-adic groups, it is interesting to have also available this former construction. Namely, the construction that we preset here is much more direct than the general construction, and it gives a number of explicit information about representations. These facts may be useful in further study of the representations of the family that we construct in this paper. It is for expecting that we shall deal a lot in future with the representations of this family, since this family includes all the generic irreducible square integrable representations (for example). From Shahidi\u27s conjecture on exsistence of a generic representation in each L2 L-packet, would follow that each L2 L-packet contains some of the representation from the family whose construction we present in this paper

Sastavljanje Hrvatske ovisnosne banke stabala: početne etape

The paper presents work–in–progress on the building of the Croatian Dependency Treebank. Its design principles, procedures and the pilot corpus used within are described. Perspectives for further development of the Croatian Dependency Treebank are presented at the end.Članak donosi međurezultate sastavljanja Hrvatske ovisnosne banke stabala koje je istraživanje u tijeku. Opisuju se njezina načela oblikovanja, postupci i uporabljeni pilot korpus. Na kraju se članka predstavljaju perspektive za daljnji razvitak Hrvatske ovisnosne banke stabala

Orbital magnetic moments in insulating Dirac systems: Impact on magnetotransport in graphene van der Waals heterostructures

In honeycomb Dirac systems with broken inversion symmetry, orbital magnetic moments coupled to the valley degree of freedom arise due to the topology of the band structure, leading to valley-selective optical dichroism. On the other hand, in Dirac systems with prominent spin-orbit coupling, similar orbital magnetic moments emerge as well. These moments are coupled to spin, but otherwise have the same functional form as the moments stemming from spatial inversion breaking. After reviewing the basic properties of these moments, which are relevant for a whole set of newly discovered materials, such as silicene and germanene, we study the particular impact that these moments have on graphene nanoengineered barriers with artificially enhanced spin-orbit coupling. We examine transmission properties of such barriers in the presence of a magnetic field. The orbital moments are found to manifest in transport characteristics through spin-dependent transmission and conductance, making them directly accessible in experiments. Moreover, the Zeeman-type effects appear without explicitly incorporating the Zeeman term in the models, i.e., by using minimal coupling and Peierls substitution in continuum and the tight-binding methods, respectively. We find that a quasiclassical view is able to explain all the observed phenomena

Spin-valley filtering in strained graphene structures with artificially induced carrier mass and spin-orbit coupling

The interplay of massive electrons with spin-orbit coupling in bulk graphene results in a spin-valley dependent gap. Thus, a barrier with such properties can act as a filter, transmitting only opposite spins from opposite valleys. In this Letter we show that strain induced pseudomagnetic field in such a barrier will enforce opposite cyclotron trajectories for the filtered valleys, leading to their spatial separation. Since spin is coupled to the valley in the filtered states, this also leads to spin separation, demonstrating a spin-valley filtering effect. The filtering behavior is found to be controllable by electrical gating as well as by strain

Changes in the agriculture of East European countries

In this article the authors attempt to present the experiences East European countries gained during the transformation of their agricultures, considering that these experiences could be of use to Croatia. They give separate accounts of the process in East Germany, Hungary, Czechoslovakia, Poland, Rumania and Bulgaria. The authors continue by examining what is now going on in West European agriculture with the purpose of avoiding mistakes that were made in the preceding period but also because both East European and Croatian agriculture are turned to the great and rich Western market that is very demanding from all aspects

Remark on representation theory of general linear groups over a non-archimedean local division algebra

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic induction. Our proofs are based on Jacquet modules (and the Geometric Lemma, incorporated in the structure of a Hopf algebra). We use only some very basic general facts of the representation theory of reductive p-adic groups (the theory that we use was completed more then three decades ago, mainly in 1970-es). Of the specific results for general linear groups over A, basically we use only a very old result of G. I. Ol’šanskii, which says that there exist complementary series starting from Ind(ρ ⊗ ρ) whenever ρ is a unitary irreducible cuspidal representation. In appendix of [11], there is also a simple local proof of these results, based on a slightly different approach