On E-functions of Semisimple Lie Groups

Details On E-functions of Semisimple Lie Groups On E-functions of Semisimple Lie Groups

2012-02-02

arxiv.org/abs/1202.0476v1

J. Phys. A: Math. Theor. 44 (2011) 325205

Physics

Mathematical Physics

17 pages, 2 figures

Scientific paper

10.1088/1751-8113/44/32/325205

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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