Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I

A strong Dixmier-Moeglin equivalence for quantum Schubert cells

Dixmier and Moeglin gave an algebraic condition and a topological condition for recognising the primitive ideals among the prime ideals of the universal enveloping algebra of a finite-dimensional complex Lie algebra; they showed that the primitive, rational, and locally closed ideals coincide. In modern terminology, they showed that the universal enveloping algebra of a finite-dimensional complex Lie algebra satisfies the Dixmier-Moeglin equivalence. We define quantities which measure how "close" an arbitrary prime ideal of a noetherian algebra is to being primitive, rational, and locally clos…

Normality of very even nilpotent varieties in D_2l

For the classical groups, Kraft and Procesi have resolved the question of which nilpotent orbits have closures which are normal and which are not, with the exception of the very even orbits in $D_{2l}$ which have partition of the form $(a^{2k}, b^2)$ for $a, b$ distinct even natural numbers with $a k + b = 2 l$. In this article, we show that these orbits do have normal closure.

Admissible modules and normality of classical nilpotent orbits I

In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a version of the Orbit Method of Kirrilov-Kostant-Souriau as proposed by Vogan. In the process we give another proof of the classification of nilpotent orbits with normal closure in the Lie algebra of a classical group first established by Kraft-Procesi.

Normality of closure of orthogonal nilpotent symmetric orbits

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is only a relatively small portion of classes with normal closure. We perform a combinatorial computation on top of the same methods used by Kraft-Procesi and Ohta.

关于幂零轨道覆盖的仿射化

On the affinization of a nilpotent orbit cover

本文研究单古典李代数中幂零伴随轨道的泛等变覆盖，将其仿射化并刻画余维2奇点，推广了Kraft–Procesi关于轨道闭包形式切片的经典结果。

极小特殊退化与对偶性

Minimal special degenerations and duality

本文分类单李代数中相邻特殊幂零轨道间 Slodowy 切片的奇点，揭示其在 Lusztig–Spaltenstein 对偶下的互换规律，并解决 Lusztig 关于切片相交上同调的猜想。