Friday, February 3, 2012

1202.0476 (Jiří Hrivnák et al.)

On E-functions of Semisimple Lie Groups    [PDF]

Jiří Hrivnák, Iryna Kashuba, Jiří Patera
We develop and describe continuous and discrete transforms of class functions
on a compact semisimple, but not simple, Lie group $G$ as their expansions into
series of special functions that are invariant under the action of the even
subgroup of the Weyl group of $G$. We distinguish two cases of even Weyl groups
-- one is the direct product of even Weyl groups of simple components of $G$,
the second is the full even Weyl group of $G$. The problem is rather simple in
two dimensions. It is much richer in dimensions greater than two -- we describe
in detail $E-$transforms of semisimple Lie groups of rank 3.
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