复杂度为1的齐性空间上不变微分算子的代数与解析性质

A note on the canonical divisor of quasi-homogeneous affine algebraic varieties

We give a necessary and sufficient condition for the canonical divisor to vanish on a quasi-homogeneous affine algebraic variety.

同调空间的代数和解析Brauer群

Algebraic and analytic Brauer groups of homogeneous spaces

本文研究了在连通、单连通、半单复代数群作用下，稳定子群闭合且连通的同调空间的代数和解析Brauer群的计算方法与主要贡献。

Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups

The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including the space of regular functions on G/H. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces G/H, where G is a simply connected non-simple semisimple complex algebraic group and H a connected closed subgroup of it. In all the cases we also find the highest weight functions corresponding to the indecomposabl…

Real points in a homogeneous space of a real algebraic group

Let G be a linear algebraic group over the field of real numbers R, and let Y be a right homogeneous space of G. We wish to find a real point of Y or to prove that Y has no real points. We describe a method to do that, implicitly using second nonabelian Galois cohomology. Our method is suitable for computer-assisted calculations.

Notes on a Lie algebraic relation

We exhibit explicit orthogonal decompositions of every multidimensional restricted root space of a real semi-simple Lie algebra. We then show a link between this result and a radiality property of smooth functions on G-homogeneous spaces when G is a real semi-simple Lie group.

齐性空间上的实子空间网与代数量子场论

Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory

本文通过将AQFT中时空区域参数化的算子代数网公理转化为实子空间网公理，从李群几何与表示论视角建立了李群幺正表示与局部代数网的联系。