Totally nonnegative and oscillatory elements in semisimple groups

DOI10.1090/S0002-9939-00-05487-3zbMath0953.22016arXivmath/9811100MaRDI QIDQ4508188

Fomin, Sergey, Andrei V. Zelevinsky

Publication date: 3 October 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9811100

zbMATH Keywords

Jacobi matricessemisimple Lie grouptotal positivitycomplex Lie grouposcillatory matrixoscillatory elementpositive minors

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15) Positive matrices and their generalizations; cones of matrices (15B48) Semisimple Lie groups and their representations (22E46) General properties and structure of complex Lie groups (22E10)

Related Items

1324- and 2143-avoiding Kazhdan–Lusztig immanants and k-positivity, On two notions of total positivity for partial flag varieties, 123, 2143-avoiding Kazhdan-Lusztig immanants and \(k\)-positive matrices, Monotonicity of strata in the stratification of the cone of totally positive matrices, \(k\)-positivity of dual canonical basis elements from 1324- and 2143-avoiding Kazhdan-Lusztig immanants, Loop-erased walks and total positivity, ON TWO CONJECTURES CONCERNING CONVEX CURVES, Bott-Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces, Cluster algebras I: Foundations, Total positivity: tests and parametrizations., In memoriam: Andrei Zelevinsky (1953--2013)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On totally positive matrices
• Total positivity and Neville elimination
• Total positivity in Schubert varieties
• A reduction theorem for totally positive matrices
• Double Bruhat cells and total positivity
• Recognizing Schubert cells.