On the existence of smooth orbital varieties in simple Lie algebras

Lucas Fresse, Anna Melnikov

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

Orbital varieties are the irreducible components of the intersection between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a reductive group. There is a geometric correspondence between orbital varieties and irreducible components of Springer fibers. In type A, a construction due to Richardson implies that every nilpotent orbit contains at least one smooth orbital variety and every Springer fiber contains at least one smooth component. In this paper, we show that this property is also true for the other classical cases. Our proof uses the interpretation of Springer fibers as varieties of isotropic flags and van Leeuwen's parametrization of their components in terms of domino tableaux. In the exceptional cases, smooth orbital varieties do not arise in every nilpotent orbit, as already noted by Spaltenstein. We however give a (nonexhaustive) list of nilpotent orbits which have this property. Our treatment of exceptional cases relies on an induction procedure for orbital varieties, similar to the induction procedure for nilpotent orbits.

اللغة الأصليةإنجليزيّة أمريكيّة
الصفحات (من إلى)960-983
عدد الصفحات24
دوريةJournal of the London Mathematical Society
مستوى الصوت101
رقم الإصدار3
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 يونيو 2020

All Science Journal Classification (ASJC) codes

  • !!Mathematics (all)

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