Polynomial invariants and harmonic functions related to exceptional regular polytopes
Iwasaki, Katsunori ; Kenma, Atsufumi ; Matsumoto, Keiji
Experiment. Math., Tome 11 (2002) no. 3, p. 313-319 / Harvested from Project Euclid
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We compute certain polynomial invariants for the finite reflection groups of the types {\small $H_3$, $H_4$ and $F_4$}. Using this result, we explicitly determine the solution space of functions satisfying a mean value property related to the exceptional regular polytopes, namely, the icosahedron and dodecahedron in three dimensions and the 24-cell, 600-cell, and 120-cell in four dimensions.
Publié le : 2002-05-14
Classification:  Polynomial invariants,  harmonic functions,  exceptional regular polytopes,  mean value property,  finite reflection groups,  52B11,  20F55 
@article{1062621224,
     author = {Iwasaki, Katsunori and Kenma, Atsufumi and Matsumoto, Keiji},
     title = {Polynomial invariants and harmonic functions related to exceptional regular polytopes},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 313-319},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1062621224}
}

Iwasaki, Katsunori; Kenma, Atsufumi; Matsumoto, Keiji. Polynomial invariants and harmonic functions related to exceptional regular polytopes. Experiment. Math., Tome 11 (2002) no. 3, pp.  313-319. http://gdmltest.u-ga.fr/item/1062621224/