Branching Law for the Finite Subgroups of $SL_4ℂ$ and the Related Generalized Poincaré Polynomials

• Date: 2015
• Main Authors: Butin, F., Бутін, Ф.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2069
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Within the framework of McKay correspondence, we determine, for every finite subgroup $Γ$ of $SL_4ℂ$, how the finite-dimensional irreducible representations of $SL_4ℂ$ decompose under the action of $Γ$. Let $\mathfrak{h}$ be a Cartan subalgebra of $\mathfrak{sl}_4ℂ$ and let $ϖ_1, ϖ_2$, and $ϖ_3$ b...