logo_acta

Acta Mathematica Vietnamica

Modular Invariant Rings and the Weyl Groups of Special Unitary Groups

icon-email Kenshi Ishiguro , Naito Nishihara

Abstract

For a compact connected Lie group G, the rational cohomology ring of its classifying space BG can be expressed as an invariant ring. Namely, for a maximal torus $T^{n}$ of G, it is well–known that $H^{*}(BG; \mathbb {Q} ) \cong H^{*}(BT^{n}; \mathbb {Q} )^{W(G)}$ which is a polynomial ring. If d divides n, the quotient $SU(n)/\mathbb {Z}_d$ is also a Lie group. Their rational cohomology rings are isomorphic, however, the integral representations of the Weyl groups $W(SU(n)/\mathbb {Z}_d)$ are not equivalent. So we ask if the modular invariant rings under the actions are polynomial. Our main theorem is a generalization of some results in [4] and [12].

Search within journal
Submit manuscript
Online first articles
Recent issues
Volumes and issues
Open access issues
Viện Hàn lâm Khoa học và Công nghệ Việt Nam Hội Toán học Việt Nam Viện Nghiên cứu Cao cấp về toán MathScinet Arxiv