Finite Chains with Quantum Affine Symmetries

We consider an extension of the (t-U) Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4^L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3^L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L states). The wave functions of the 3^L-state system are obtained explicitly from those of the 2^L-state system, and the degeneracies can be understood in terms of irreducible representations of U_q(\hat{sl(2)}).Comment: 31pp, Latex, CERN-TH.6935/93. To app. in Int. Jour. Mod. Phys. A. (The title of the paper is changed. This is the ONLY change. Previous title was: Hubbard-Like Models in the Infinite Repulsion Limit and Finite-Dimensional Representations of the Affine Algebra U_q(\hat{sl(2)}).

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde

Conference: 51st Meeting of Lawyers in Opatija

U radu se prikazuje 51. susret pravnika u Opatiji, odrzan od 15. do 17. svibnja 2013

Deformation of orthosymplectic Lie superalgebra osp(1|2)

Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is defined by chains of twists. Corresponding classical r-matrix is obtained by a contraction procedure from the trigonometric r-matrix. The carrier space of the constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page

ETHYLENE RESPONSE FACTOR 115 integrates jasmonate and cytokinin signaling machineries to repress adventitious rooting in Arabidopsis

Adventitious root initiation (ARI) is ade novoorganogenesis program and a key adaptive trait in plants. Several hormones regulate ARI but the underlying genetic architecture that integrates the hormonal crosstalk governing this process remains largely elusive. In this study, we use genetics, genome editing, transcriptomics, hormone profiling and cell biological approaches to demonstrate a crucial role played by the APETALA2/ETHYLENE RESPONSE FACTOR 115 transcription factor. We demonstrate that ERF115 functions as a repressor of ARI by activating the cytokinin (CK) signaling machinery. We also demonstrate thatERF115is transcriptionally activated by jasmonate (JA), an oxylipin-derived phytohormone, which represses ARI in NINJA-dependent and independent manners. Our data indicate that NINJA-dependent JA signaling in pericycle cells blocks early events of ARI. Altogether, our results reveal a previously unreported molecular network involving cooperative crosstalk between JA and CK machineries that represses ARI