6 papers
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 th…
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…
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
Yuhan Peng, Junwen Dong, Yuzhi Zeng +6
Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (direc…
Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups
J. Maxwell Riestenberg, Diaaeldin Taha, Steve Trettel +1
We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups, called C-47, and C-55 in the paper \cite{BajpaiDonaNitsche2025Thin} by Bajpai-Dona-Nitsche. Th…
Positivity and Non-commutativity
Anna Wienhard
In this article we revisit a new notion of positivity in real semisimple Lie groups that at the same time generalizes total positivity in split real Lie groups as well as positive…
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 ord…