Journal of Lie Theory

no. 1
The affine root system of an isoparametric submanifold in Hilbert space
Gorodski, Claudio1; Heintze, Ernst2
1Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP 05509-090, Brazil
2Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 43-49

An alternative construction of the affine root system of an isoparametric submanifold in Hilbert space to that in [5] is provided, without invoking Dadok’s theorem.

Received:
Accepted:
Published online:
DOI: 10.5802/jolt.1418
Classification: 58B25, 53C35, 17B22, 51F15
Keywords: Coxeter groups, affine root systems, isoparametric submanifolds

Gorodski, Claudio  1 ; Heintze, Ernst  2

1 Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP 05509-090, Brazil
2 Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany 
Gorodski, Claudio; Heintze, Ernst. The affine root system of an isoparametric submanifold in Hilbert space. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 43-49. doi: 10.5802/jolt.1418
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[1] Bourbaki, Nicolas Éléments de mathématique: Groupes et algèbres de Lie, Fascicule XXXIV, Chapitres IV, V, VI: Groupes de Coxeter et systèmes de Tits. Groupes engendrés par des réflexions. Systèmes de racines, Actualités Scientifiques et Industrielles, 1337, Hermann, 1968 | Zbl

[2] Bruhat, François; Tits, Jacques Groupes réductifs sur un corps local, Publ. Math., Volume 41 (1972), pp. 5-251 | Numdam | DOI | Zbl

[3] Dadok, Jiri Polar coordinates induced by actions of compact Lie groups, Trans. Am. Math. Soc., Volume 288 (1985), pp. 125-137 | MR | DOI | Zbl

[4] Eschenburg, Jost-Hinrich; Heintze, Ernst Polar representations and symmetric spaces, J. Reine Angew. Math., Volume 507 (1999), pp. 93-106 | MR | DOI | Zbl

[5] Gorodski, Claudio; Heintze, Ernst Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space, J. Fixed Point Theory Appl., Volume 11 (2012) no. 1, pp. 93-136 | Zbl | DOI | MR

[6] Heintze, Ernst Toward symmetric spaces of affine Kac–Moody type, Int. J. Geom. Methods Mod. Phys., Volume 3 (2006) no. 5-6, pp. 881-898 | DOI | Zbl | MR

[7] Heintze, Ernst; Liu, Xiaobo Homogeneity of infinite-dimensional isoparametric submanifolds, Ann. Math. (2), Volume 149 (1999) no. 1, pp. 149-181 | DOI | Zbl

[8] Heintze, Ernst; Olmos, Carlos Normal holonomy groups and s-representations, Indiana Univ. Math. J., Volume 41 (1992) no. 3, pp. 869-874 | DOI | Zbl | MR

[9] Macdonald, Ian G. Affine root systems and Dedekind’s η-function, Invent. Math., Volume 15 (1971), pp. 91-143 | DOI | Zbl | MR

[10] Terng, Chuulian Proper Fredholm submanifolds of Hilbert space, J. Differ. Geom., Volume 29 (1989) no. 1, pp. 9-47 | Zbl | DOI | MR

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