Abstract
The intersection between a nilpotent orbit O∪gln(C) and the Lie algebra Lie(B)∪gln(C) of a Borel subgroup B∪GLn(C) is an equidimensional, quasi-affine algebraic variety. Its irreducible components are called orbital varieties. In this Note, we provide criteria to guarantee that an orbital variety is smooth or has a dense orbit for the adjoint action of B. In addition, we point out a possible relation between these two properties.
Original language | English |
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Pages (from-to) | 735-739 |
Number of pages | 5 |
Journal | Comptes Rendus Mathematique |
Volume | 349 |
Issue number | 13-14 |
DOIs | |
State | Published - Jul 2011 |
Bibliographical note
Funding Information:E-mail addresses: [email protected] (L. Fresse), [email protected] (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.
ASJC Scopus subject areas
- General Mathematics