Reflection algebras for sl(2) and gl(1|1)

We present a generalization the G. Letzter's theory of quantum symmetric pairs of semisimple Lie algebras for the case of quantum affine algebras. We then study solutions of the reflection equation for the quantum affine algebras sl(2) and gl(1|1) and their Yangian limit for singlet (diagonal) and vector (non-diagonal) boundary conditions. We construct the corresponding quantum affine coideal subalgebras that are based on the quantum symmetric pairs, and the (generalized) twisted Yangians.Comment: 31 page; v2: updated versio

Yangian of AdS3/CFT2 and its deformation

We construct highest-weight modules and a Yangian extension of the centrally extended sl(1|1)^2 superalgebra, that is a symmetry of the worldsheet scattering associated with the AdS3/CFT3 duality. We demonstrate that the R-matrix intertwining atypical modules is of a trigonometric type. We also consider a quantum deformation of this superalgebra, its modules, and obtain a quantum affine extension of the Drinfeld-Jimbo type that describes a deformed worldsheet scattering.Comment: 21 pages, 1 figure. Final version. Accepted to J. Geom. and Phy

Yangian symmetry of the Y=0 maximal giant graviton

We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from boundaries with no degrees of freedom. We present the generalized twisted boundary Yangian of open strings ending on boundaries which preserve only a subalgebra h of the bulk algebra g, where (g,h) is a symmetric pair. This is realized by open strings ending on the D3 brane known as the Y=0 maximal giant graviton in AdS_5 x S^5. We also consider the Yangian symmetry of the boundary which preserves an su(1|2) subalgebra only.Comment: 17 pages, v2: minor correction made, accepted for publication in JHE

On boundary fusion and functional relations in the Baxterized affine Hecke algebra

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.Comment: 35 pages, 3 figure

Integrable open spin-chains in AdS3/CFT2 correspondences

We study integrable open boundary conditions for d(2,1;\alpha)^2 and psu(1,1|2)^2 spin-chains. Magnon excitations of these open spin-chains are mapped to massive excitations of type IIB open superstrings ending on D-branes in the AdS_3 x S^3 x S^3 x S^1 and AdS_3 x S^3 x T^4 supergravity geometries with pure R-R flux. We derive reflection matrix solutions of the boundary Yang-Baxter equation which intertwine representations of a variety of boundary coideal subalgebras of the bulk Hopf superalgebra. Many of these integrable boundaries are matched to D1- and D5-brane maximal giant gravitons.Comment: v1: 61 pages, 6 figures; v2: minor changes and reference added; v3: minor changes, 60 pages, version accepted to journa

Vertex Representations for Yangians of Kac-Moody algebras

30 pagesUsing vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.Peer reviewe

Lietuvos katalikų bažnyčių metrikų knygų tyrimo gairės

The metrics books of the Lithuanian Catholic Church are a heritage treasure of the whole nation. Up until the 20th century there were approximately 600 churches in Lithuania and each church had more than a dozen metrics books on average which means there could be up to 10 000–15 000 metrics books remaining in various archives. Due to the soviet occupation the church archives were damaged and metrics books were scattered to various unclear locations. Due to these unfortunate historical situation metrics books research has only begun and the books themselves are not yet fully catalogued. Some research on metrics books has been done by Zigmas Zinkevičius, Vitalija Macijauskienė, Jonas Palionis and others. Historians have shed some light on metrics book archives in various archives. It is clear that individual important research work has been done but an overall targeted research is lacking. A priority objective is to create a state wide data base of all catalogued metrics books. Second steps would be complex research of the metrics books including creation of a theoretical information base, creation of various data bases, use of the metrics books for localized research and etc. Successful research of metrics books is only possible if specific guidelines are followed. That is why this publication includes methodical instructions for researches to use when uncertain situations are encountered. The publication includes two cases of metrics books research. In the first example a couple of unique excerpts are presented with comments. The second one reconstructs the picture of the Suginčiai (Molėtai district) estate and town community during the 17th century. It includes residents of the estate, newlyweds, families and other persons). Philological notes on names are also included.Straipsnyje pateikiama žinių apie Lietuvos katalikų bažnyčių metrikų knygas, jų archyvus, parodoma jų vertė. Supažindinama su metrikų knygų tyrimo problemomis, pateikiama metodinių rekomendacijų metrikų knygų tyrėjams, atskleidžiama, kaip metrikų knygų medžiagą galima panaudoti tyrimams. Pateikta ir pakomentuota keletas išsiskiriančių metrikų įrašų, iš Molėtų XVII a. pabaigos metrikų knygų rekonstruota Suginčių (dvaro ir kaimo) XVII a. pabaigos bendruomenė

Acquisition and Forensic Analysis of Volatile Data Stores

The advent of more witted threats against typical computer systems demonstrates a need for forensic analysis of memory-resident data in addition to the conventional static analysis common today. Some tools are starting to become available to duplicate various types of volatile data stores. Once the data store has been duplicated, current forensic procedures have no vector for extrapolating further information from the duplicate. This thesis is focused on providing the groundwork for performing forensic investigations on the data that is typically stored in a volatile data store, such as system RAM, while creating as small an impact as possible to the state of a system. It is intended that this thesis will give insight to obtaining more post incident response information along with a smaller impact to potential evidence when compared to typical incident response procedures