TY - JOUR
T1 - On geometric properties of orbital varieties in type A
AU - Fresse, Lucas
AU - Melnikov, Anna
N1 - Funding Information: E-mail addresses: [email protected] (L. Fresse), [email protected] (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.
PY - 2011/7
Y1 - 2011/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80051556891&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.crma.2011.05.016
DO - https://doi.org/10.1016/j.crma.2011.05.016
M3 - Article
SN - 1631-073X
VL - 349
SP - 735
EP - 739
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 13-14
ER -