Good representations and solvable groups

Solvable Groups, Free Divisors and Nonisolated Matrix Singularities I: Towers of Free Divisors

We introduce a method for obtaining new classes of free divisors from representations $V$ of connected linear algebraic groups $G$ where $\dim(G)=\dim(V)$, with $V$ having an open orbit. We give sufficient conditions that the complement of this open orbit, the "exceptional orbit variety", is a free divisor (or a slightly weaker free* divisor) for "block representations" of both solvable groups and extensions of reductive groups by them. These are representations for which the matrix defined from a basis of associated "representation vector fields" on $V$ has block triangular form, with blocks …

Singularity of the varieties of representations of lattices in solvable Lie groups

For a lattice $Γ$ of a simply connected solvable Lie group $G$, we describe the analytic germ in the variety of representations of $Γ$ at the trivial representation as an analytic germ which is linearly embedded in the analytic germ associated with the nilpotent Lie algebra determined by $G$. By this description, under certain assumption, we study the singularity of the analytic germ in the variety of representations of $Γ$ at the trivial representation by using the Kuranishi space construction. By a similar technique, we also study deformations of holomorphic structures of trivial vector bund…

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H.

整数上水平除子的可解覆盖扩张

Extension of solvable coverings across horizontal divisors over the integers

本文研究算术概形删除水平除子后平展基本群的变化，在正则性等条件下证明核拓扑完美，从而最大可解商同构，并应用于超平面补集与表示扩张。