论文标题
双环组和弗罗贝尼乌斯歧管
Dicyclic groups and Frobenius manifolds
论文作者
论文摘要
有限基团的不可减至表示的轨道空间是一种变体，其坐标环由均匀不变多项式有限生成。鲍里斯·杜布罗温（Boris Dubrovin）表明，反射组的轨道空间获得了多项式Frobenius歧管的结构。 Dubrovin在轨道空间上构建Frobenius歧管的示例的方法是为离散基团的其他线性表示的，这些线性具有共同点，即轨道空间的坐标环是多项式环。在本文中，我们表明，二环类群的不可还原表示的轨道空间获得了Frobenius歧管的两个结构。该轨道空间的坐标环不是多项式环。
The orbits space of an irreducible representation of a finite group is a variety whose coordinate ring is finitely generated by homogeneous invariant polynomials. Boris Dubrovin showed that the orbits spaces of the reflection groups acquire the structure of polynomial Frobenius manifolds. Dubrovin's method to construct examples of Frobenius manifolds on orbits spaces was carried for other linear representations of discrete groups which have in common that the coordinate rings of the the orbits spaces are polynomial rings. In this article, we show that the orbits space of an irreducible representation of a Dicyclic group acquire two structures of Frobenius manifolds. The coordinate ring of this orbits space is not a polynomial ring.
