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Article: Product structure and regularity theorem for totally nonnegative flag varieties
Title | Product structure and regularity theorem for totally nonnegative flag varieties |
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Authors | |
Issue Date | 9-Apr-2024 |
Publisher | Springer |
Citation | Inventiones Mathematicae, 2024, v. 237, n. 1, p. 1-47 How to Cite? |
Abstract | The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) J-total positivity on the full flag variety of an arbitrary Kac-Moody group, generalizing the (ordinary) total positivity. We show that the J-totally nonnegative flag variety has a cellular decomposition into totally positive J-Richardson varieties. Moreover, each totally positive J-Richardson variety admits a favorable decomposition, called a product structure. Combined with the generalized Poincare conjecture, we prove that the closure of each totally positive J-Richardson variety is a regular CW complex homeomorphic to a closed ball. Moreover, the J-total positivity on the full flag provides a model for the (ordinary) totally nonnegative partial flag variety. As a consequence, we prove that the closure of each (ordinary) totally positive Richardson variety is a regular CW complex homeomorphic to a closed ball, confirming conjectures of Galashin, Karp and Lam in (Adv. Math. 351:614–620, 2019). We also show that the link of the totally nonnegative part of U− for any Kac-Moody group forms a regular CW complex. This generalizes the result of Hersh (Invent. Math. 197(1):57–114, 2014) for reductive groups. |
Persistent Identifier | http://hdl.handle.net/10722/347539 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 4.321 |
DC Field | Value | Language |
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dc.contributor.author | Bao, Huanchen | - |
dc.contributor.author | He, Xuhua | - |
dc.date.accessioned | 2024-09-25T00:30:36Z | - |
dc.date.available | 2024-09-25T00:30:36Z | - |
dc.date.issued | 2024-04-09 | - |
dc.identifier.citation | Inventiones Mathematicae, 2024, v. 237, n. 1, p. 1-47 | - |
dc.identifier.issn | 0020-9910 | - |
dc.identifier.uri | http://hdl.handle.net/10722/347539 | - |
dc.description.abstract | <p>The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) J-total positivity on the full flag variety of an arbitrary Kac-Moody group, generalizing the (ordinary) total positivity. We show that the J-totally nonnegative flag variety has a cellular decomposition into totally positive J-Richardson varieties. Moreover, each totally positive J-Richardson variety admits a favorable decomposition, called a product structure. Combined with the generalized Poincare conjecture, we prove that the closure of each totally positive J-Richardson variety is a regular CW complex homeomorphic to a closed ball. Moreover, the J-total positivity on the full flag provides a model for the (ordinary) totally nonnegative partial flag variety. As a consequence, we prove that the closure of each (ordinary) totally positive Richardson variety is a regular CW complex homeomorphic to a closed ball, confirming conjectures of Galashin, Karp and Lam in (Adv. Math. 351:614–620, 2019). We also show that the link of the totally nonnegative part of U<sup>−</sup> for any Kac-Moody group forms a regular CW complex. This generalizes the result of Hersh (Invent. Math. 197(1):57–114, 2014) for reductive groups.<br></p> | - |
dc.language | eng | - |
dc.publisher | Springer | - |
dc.relation.ispartof | Inventiones Mathematicae | - |
dc.title | Product structure and regularity theorem for totally nonnegative flag varieties | - |
dc.type | Article | - |
dc.identifier.doi | 10.1007/s00222-024-01256-2 | - |
dc.identifier.volume | 237 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 47 | - |
dc.identifier.eissn | 1432-1297 | - |
dc.identifier.issnl | 0020-9910 | - |