Quantum R-matrix and Intertwiners for the Kashiwara Algebra

We study the algebra $B_q(\ge)$ presented by Kashiwara and introduce intertwiners similar to $q$-vertex operators. We show that a matrix determined by 2-point functions of the intertwiners coincides with a quantum R-matrix (up to a diagonal matrix) and give the commutation relations of the intertwiners. We also introduce an analogue of the universal R-matrix for the Kashiwara algebra.Comment: 21 page

The sl_3 web algebra

In this paper we use Kuperberg’s sl3-webs and Khovanov’s sl3-foams to define a new algebra KS, which we call the sl3-web algebra. It is the sl3 analogue of Khovanov’s arc algebra. We prove that KS is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of q-skew Howe duality, which allows us to prove that KS is Morita equivalent to a certain cyclotomic KLR-algebra of level 3. This allows us to determine the split Grothendieck group K0 (WS )Q(q) , to show that its center is isomorphic to the cohomology ring of a certain Spaltenstein variety, and to prove that KS is a graded cellular algebra.info:eu-repo/semantics/publishedVersio

Discommensurations, modulated phases and lock-in transitions of thiourea

The modulated phases and the successive phase transition of thiourea are reinvestigated by means of dielectric measurements and X-ray scatterings. In the E-T phase diagram, eightfold and ninefold superstructures are designated in h-thiourea. There remain some discommensurations as domain walls in the ferroelectric phase. The structure of discommensurations is discussed based on the structural analysis of the superstructures at -95℃ and -103℃