Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 1 (2005), 025, 6 pages      math-ph/0512029      http://dx.doi.org/10.3842/SIGMA.2005.025

Compact Simple Lie Groups and Their C-, S-, and E-Transforms

Jiri Patera
Centre de Recherches Mathématiques, Université de Montréal, C.P.6128-Centre ville, Montréal, H3C 3J7, Québec, Canada

Received December 01, 2005; Published online December 09, 2005

Abstract
New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank 2 ≤ n < ∞. Rank 1 transforms are known. Rank 2 exposition of C- and S-transforms is in the literature. The E-transforms appear here for the first time.

Key words: compact simple Lie groups; C-, S-, and E-transforms; discretization; fundamental region; Weyl group; weight lattice.

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References

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