Reductive Group Actions and Their Invariants

本文拟研究仿射空间的构造不变理论、与约化群相关的广义颤振和自同构等领域的问题。在第一种情况下，提出将改进他的算法来计算约简群不变量；第二，与Weyman一起，将颤振表示应用于约化群；在最后一种情况下看看仿射空间在复数上的自同构。约化群理论有助于从代数的角度研究空间的各种对称性。在化学和物理中也有应用。

ROTA/DERKSEN, 9970165The proposer plans to investigate problems in the areas of constructive invariant theory, generalized quivers associated to reductive groups and automorphisms of affine spaces. In the first case the proposerwill refine his algorithm for computing reductive group invariants; in the second, with Weyman, apply quiver representations to reductive groups; in the last case look at automorphisms of affine space over the complex numbers. The theory of reductive groups aids in studying various symmetry properties of space from an algebraic point of view. Applications are to be found in chemistry and physics.