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.
Bibliographical noteFunding Information:
E-mail addresses: firstname.lastname@example.org (L. Fresse), email@example.com (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.
ASJC Scopus subject areas
- Mathematics (all)