The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(ŝl`). It has a standard basis indexed by partitions and the non-zero matrix entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial Weyl modules for Uq(glN ) as N tends to infinity. We explain how the powers of v which appear in t...

A theoretical foundation for a generalization of the elliptic difference Painlevé equation to higher dimensions is provided in the framework of birational Weyl group action on the space of point configurations in general position in a projective space. By introducing an elliptic parametrization of point configurations, a realization of the Weyl group is proposed as a group of Cremona transforma...

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite ch...

A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...