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Criteria for rational smoothness of some symmetric orbit closures
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: DMTCS Proceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, 319-330 p.Conference paper, Published paper (Refereed)
Abstract [en]

Let G be a connected reductive linear algebraic group over ℂ with an involutionθ. Denote by K the subgroup of fixed points. In certain cases, the K-orbits in the flag variety G/B are indexed by the twisted identities ι(θ) = {θ (w -1)w |w ∈ W} in the Weyl group W. Under this assumption, we establish a criterion for rational smoothness of orbit closures which generalises classical results of Carrell and Peterson for Schubert varieties. That is, whether an orbit closure is rationally smooth at a given point can be determined by examining the degrees in a "Bruhat graph" whose vertices form a subset of ι(θ). Moreover, an orbit closure is rationally smooth everywhere if and only if its corresponding interval in the Bruhat order on ι(θ) is rank symmetric. In the special case K = Sp 2n(ℂ), G = SL 2n(ℂ), we strengthen our criterion by showing that only the degree of a single vertex, the "bottom one", needs to be examined. This generalises a result of Deodhar for type A Schubert varieties.

Place, publisher, year, edition, pages
2010. 319-330 p.
Keyword [en]
Bruhat graph, Rational smoothness, Symmetric orbit
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-150314Scopus ID: 2-s2.0-84860541566OAI: oai:DiVA.org:kth-150314DiVA: diva2:742431
Conference
22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10, 2 August 2010 through 6 August 2010, San Francisco, CA, United States
Note

QC 20140901

Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2014-09-01Bibliographically approved

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CiteExportLink to record
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  • apa
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