On orbital variety closures in \(\mathfrak{sl}_n\). I: Induced Duflo order.

DOI10.1016/j.jalgebra.2003.09.012zbMath1077.17008arXivmath/0311472OpenAlexW2061536309MaRDI QIDQ1421801

Anna Melnikov

Publication date: 3 February 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311472

zbMATH Keywords

semisimple algebraic groupsnilpotent orbitsorbital varietiesDuflo orderRobinson-Schensted procedure

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Classical groups (algebro-geometric aspects) (14L35)

Related Items (11)

CORRESPONDENCE BETWEEN ORBITAL VARIETIES AND SETS OF SUBSPACES STABLE UNDER NILPOTENT ENDOMORPHISM ⋮ On orbital variety closures in \(\mathfrak{sl}_n\). III: Geometric properties ⋮ Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid. ⋮ On orbital variety closures in \(\mathfrak{sl}_n\). II: Descendants of a Richardson orbital variety. ⋮ Primitive elements of the Hopf algebras of tableaux ⋮ Inner tableau translation property of the weak order and related results ⋮ On intersections of orbital varieties and components of Springer fiber ⋮ Properties of four partial orders on standard Young tableaux ⋮ Young-Fibonacci insertion, tableauhedron and Kostka numbers ⋮ Hopf algebras of \(m\)-permutations, \((m + 1)\)-ary trees, and \(m\)-parking functions ⋮ On varieties in an orbital variety closure in semisimple Lie algebras

Cites Work

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• Singularities in the Nilpotent Scheme of a Classical Group
• La correspondance de Robinson

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