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 Uspekhi Mat. Nauk, 1988, Volume 43, Issue 3(261), Pages 125–160 (Mi umn1892)

Wavefronts and reflection groups

O. P. Shcherbak

Abstract: Typical singularities of wave fronts and ray systems passing by smooth obstacle in $3$-space are described in the article. These singularities turn out to be connected with noncristallographic Coxeter groups $I_2(5)$, $H_3$, $H_4$. Proofs are based on the detail in­vestigation of the discriminants of these groups by their inclusion into cristallographic ones $A_4$, $D_6$, $E_8$ correspondently. Besides, there is given a geometrical description of some singularities of bicaustics in collisionless flows of particles. It is based on inclu­sions of Coxeter groups $A_1^\mu$, $D_\mu$, $D_4$ into $B_\mu$, $G_\mu$, $F_4$ as normal subgroups. The article contains a wide table matherial on neutral stratification of discriminants of reflection groups.
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English version:
Russian Mathematical Surveys, 1988, 43:3, 149–194

Bibliographic databases:

UDC: 514.8
MSC: 20F55, 51F15

Citation: O. P. Shcherbak, “Wavefronts and reflection groups”, Uspekhi Mat. Nauk, 43:3(261) (1988), 125–160; Russian Math. Surveys, 43:3 (1988), 149–194

Citation in format AMSBIB
\Bibitem{Shc88}
\by O.~P.~Shcherbak
\paper Wavefronts and reflection groups
\jour Uspekhi Mat. Nauk
\yr 1988
\vol 43
\issue 3(261)
\pages 125--160
\mathnet{http://mi.mathnet.ru/umn1892}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=955776}
\zmath{https://zbmath.org/?q=an:0675.58007}
\transl
\jour Russian Math. Surveys
\yr 1988
\vol 43
\issue 3
\pages 149--194
\crossref{https://doi.org/10.1070/RM1988v043n03ABEH001741}

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