An important problem arising in the representation theory of a Lie group or Lie algebra, and
especially in physical applications, is the determination of the invariant functions of its …

The concept of a graded Lie ring L is studied systematically. A grading of L is defined as a
decomposition of the additive group of L into a direct sum with simple multiplicative behavior …

In the paper, properties of orbit functions are reviewed and further developed. Orbit functions
on the Euclidean space E n are symmetrized exponential functions. The symmetrization is …

The purpose of this article is to find all Lie subalgebras of all real Lie algebras of dimension
d", 4. More precisely, we shall classify the subalgebras of each such Lie algebra into …

We present a general method for reducing the problem of finding all continuous subgroups
of a given Lie group G with a nontrivial invariant subgroup N, to that of classifying the …

Unique affine extensions H aff 2, H aff 3 and H aff 4 are determined for the noncrystallographic
Coxeter groups H 2, H 3 and H 4. They are used for the construction of new mathematical …

A family of quasicrystals of dimensions 1, 2, 3, 4 governed by the root lattice E 8 is constructed.
The use of the icosian ring, found in the quaternions with coefficients in Q (square root 5), …

The paper contains a generalization of known properties of Chebyshev polynomials of the
second kind in one variable to polynomials of n variables based on the root lattices of …

00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody
algebras. It is the result of an unusual interdisciplinary effort by two physicists and two …

To obtain fine gradings of gl(n,C), it is necessary to study maximal Abelian subgroups (MAD-subgroups)
of diagonizable automorphisms in A ut(gl(n,C)). We described two finite sets H n …