We give a condition ensuring that the operators in nilpotent Lie algebra of linear on finite dimensional vector space have common eigenvector.

Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a Gmodule. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits. Thesis Supervisor: David Alexander Vogan Title: Professor of Mathematics

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The classification is the same as in the characteristic zero case obtained by D.I. Panyushev in 1994, [32]: for e a nilpotent element in the Lie algebra of G, the ...

We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie a...

If X is the complement of a hypersurface in P, then Kohno showed in [9] that the nilpotent completion of π1(X) is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks φk of the lower central series quotients of π1(X) are known in only two very special cases: if X is hypersolvable (in which case the quadratic c...

In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra n3 and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of n3 with the versal base.

This paper studies restricted modules of gap-p Virasoro algebra gp and their intrinsic connection to twisted certain vertex algebras. We first establish an equivalence between the category gp-modules level ℓ_ VNp(ℓ_,0), where Np is a new Lie algebra, ℓ_:=(ℓ0,0,⋯,0)∈C[p2]+1, ℓ0∈C action center. Then we focus on construction classification simple ℓ_. More explicitly, give uniform as induced modul...

We prove that the maximal nilpotent subalgebra of a Kac-Moody Lie algebra has a (essentially, unique) Euclidean metric with respect to which the Laplace operator in the chain complex is scalar on each component of a given degree. Moreover, both the Lie algebra structure and the metric are uniquely determined by this property.

Let G be a connected linear semisimple Lie group with Lie algebra g, and let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that Ω is a nilpotent G-orbit in g and O is the nilpotent K C -orbit in p C associated to Ω by the Kostant-Sekiguchi correspondence. We show that the complexity of O as a K C variety measures ...