On the algebra A_{\hbar,\eta}(osp(2|2)^{(2)}) and free boson representations

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current algebra with the structure of a so-called infinite Hopf family of (super)algebras. A representation of this algebra at $c=1$ is realized in the product Fock space of two commuting sets of Heisenberg algebras.Comment: 14 pages, LaTe

q-deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.Comment: LaTex file 18 page

Eigenvalues of Ruijsenaars-Schneider models associated with An−1A_{n-1} root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].Comment: Latex file, 25 page

Propagating wave in active region-loops, located over the solar disk observed by the Interface Region Imaging Spectrograph

We aim to ascertain the physical parameters of a propagating wave over the solar disk detected by the Interface Region Imaging Spectrograph (IRIS). Using imaging data from the IRIS and the Solar Dynamic Observatory (SDO), we tracked bright spots to determine the parameters of a propagating transverse wave in active region (AR) loops triggered by activation of a filament. Deriving the Doppler velocity of Si IV line from spectral observations of IRIS, we have determined the rotating directions of active region loops which are relevant to the wave. On 2015 December 19, a filament was located on the polarity inversion line of the NOAA AR 12470. The filament was activated and then caused a C 1.1 two-ribbon flare. Between the flare ribbons, two rotation motions of a set of bright loops were observed to appear in turn with opposite directions. Following the end of the second rotation, a propagating wave and an associated transverse oscillation were detected in these bright loops. In 1400 A channel, there was bright material flowing along the loops in a wave-like manner, with a period of ~128 s and a mean amplitude of ~880 km. For the transverse oscillation, we tracked a given loop and determine the transverse positions of the tracking loop in a limited longitudinal range. In both of 1400 A and 171 A channels, approximately four periods are distinguished during the transverse oscillation. The mean period of the oscillation is estimated as ~143 s and the displacement amplitude as between ~1370 km and ~690 km. We interpret these oscillations as a propagating kink wave and obtain its speed of ~1400 km s-1. Our observations reveal that a flare associated with filament activation could trigger a kink propagating wave in active region loops over the solar disk.Comment: Accepted for publication in A&

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.Comment: 23 page

Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two references to Awata,H. et al adde