On a certain generator system of the ring of invariants of a finite reflection group

DOI10.1080/00927878008822464zbMath0428.14020OpenAlexW2062268568MaRDI QIDQ3864639

Kyoji Saito, Jiro Sekiguchi, Tamaki Yano

Publication date: 1980

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927878008822464

zbMATH Keywords

ring of invariants symmetric algebra finite Coxeter group generator system finite group generated by reflections

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Other geometric groups, including crystallographic groups (20H15) Reflection groups, reflection geometries (51F15)

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Cites Work