we characterize the rational subsets of a finite group and discuss the relations to integral cayley graphs.

The representation theory of Kac–Moody algebras, and in particular that of affine Lie algebras, has been extensively studied over the past twenty years. The representations that have had the most applications are the integrable ones, so called because they lift to the corresponding group. The affine Lie algebra associated to a finite-dimensional complex simple Lie algebra g is the universal (on...

Let G be a simple algebraic group of type A or D defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T -fixed point subscheme (Gr λ G) T of the Schubert variety Gr λ G in the affine Grassmannian GrG is a finite scheme. We prove that there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (...

Abstract This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The material is considered made by isotropic matrix with embedded fibers, each component having its own relaxation dynamics. constitutive equations are provided in terms free energy density and dissipation density, which both required to be thermodynamically ...

For any finite graph Γ and any field K of characteristic unequal to 2 we construct an algebraic variety X over K whose K-points parameterise K-Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with prescribed commutation relations, corresponding to the non-edges. After that, we study the case where Γ is a connected, simply laced Dynkin diagram of finite or...