Lattice Representations of Heisenberg Groups

Vertex Representations via Finite Groups and the Mckay Correspondence

where the first factor is a symmetric algebra and the second one is a group algebra. The affine algebra ĝ contains a Heisenberg algebra ĥ. One can define the so-called vertex operators X(α, z) associated to α ∈ Q acting on V essentially using the Heisenberg algebra ĥ. The representation of ĝ on V is then obtained from the action of the Heisenberg algebra ĥ and the vertex operators X(α, z) assoc...

Random Walk Representations of the Heisenberg Model

In this paper we develop some random walk representations for the spin-S Heisenberg ferromagnet with nearest neighbor interaction on the integer lattice in d dimensions. The representations parallel corresponding representations for the perfect Bose gas. Hence the Heisenberg model can be thought of as an interacting Bose gas. This has been made more explicit in the paper of Dyson (5/ (see also ...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

مطالعه مدل هایزنبرگ به روش خودسازگار گاؤسی بر روی شبکه‌ها‌ی لانه زنبوری و الماسی

The classical J1-J2 Heisenberg model on bipartite lattice exhibits "Neel" order. However if the AF interactions between the next nearest neighbor(nnn) are increased with respect to the nearest neighbor(nn), the frustration effect arises. In such situations, new phases such as ordered phases with coplanar or spiral ordering and disordered phases such as spin liquids can arise. In this paper we ...

EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations

GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...