3 research outputs found
Six types of functions of the Lie groups O(5) and G(2)
New families of -functions are described in the context of the compact
simple Lie groups O(5) and G(2). These functions of two real variables
generalize the common exponential functions and for each group, only one family
is currently found in the literature. All the families are fully characterized,
their most important properties are described, namely their continuous and
discrete orthogonalities and decompositions of their products.Comment: 25 pages, 13 figure
On E-functions of Semisimple Lie Groups
We develop and describe continuous and discrete transforms of class functions
on a compact semisimple, but not simple, Lie group as their expansions into
series of special functions that are invariant under the action of the even
subgroup of the Weyl group of . We distinguish two cases of even Weyl groups
-- one is the direct product of even Weyl groups of simple components of ,
the second is the full even Weyl group of . The problem is rather simple in
two dimensions. It is much richer in dimensions greater than two -- we describe
in detail transforms of semisimple Lie groups of rank 3.Comment: 17 pages, 2 figure
Gaussian cubature arising from hybrid characters of simple Lie groups
Lie groups with two different root lengths allow two mixed sign homomorphisms
on their corresponding Weyl groups, which in turn give rise to two families of
hybrid Weyl group orbit functions and characters. In this paper we extend the
ideas leading to the Gaussian cubature formulas for families of polynomials
arising from the characters of irreducible representations of any simple Lie
group, to new cubature formulas based on the corresponding hybrid characters.
These formulas are new forms of Gaussian cubature in the short root length case
and new forms of Radau cubature in the long root case. The nodes for the
cubature arise quite naturally from the (computationally efficient) elements of
finite order of the Lie group.Comment: 23 pages, 3 figure