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math.DG2026
Generalizing Lusztig's total positivity II : geometric properties
Olivier Guichard, Anna Wienhard
Positive structures in Lie groups with respect to a subset of the set of positive roots provide a generalization of Lusztig's total positivity in split real Lie groups to the s…
math.DG2025
Symmetric spaces for groups over involutive algebras and applications to Higgs bundles
Pengfei Huang, Georgios Kydonakis, Eugen Rogozinnikov +1
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras . In the case when the algebra is Hermitian, or the…
math.DG2022★ 1 cited
Generalizing Lusztig's total positivity
Olivier Guichard, Anna Wienhard
We introduce the notion of -positivity in real simple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orde…