2013/07/09 by Frédéric Butin, Butin, Frédéric
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1307.2557
9 pages
arxiv created 2013/07/09 · openalex publication_date 2013/07/09 · arxiv updated 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of McKay correspondence we determine, for every finite subgroup Γ of SL4ℂ, how the finite dimensional irreducible representations of SL4ℂ decompose under the action of Γ. Let \goh be a Cartan subalgebra of \gosl4ℂ and let \varpi1, \varpi2, \varpi3 be the corresponding fundamental weights. For (p,q,r)∈ ℕ3, the restriction πp,q,r|Γ of the irreducible representation πp,q,r of highest weight p\varpi1+q\varpi2+r\varpi3 of SL4ℂ decomposes as πp,q,r|Γ=\bigoplusi=0l mi(p,q,r)γi. We determine the multiplicities mi(p,q,r) and prove that the series PΓ(t,u,w)i=∑p=0^∞∑q=0^∞∑r=0^∞ mi(p,q,r)tpuqwr are rational functions. This generalizes results from Kostant for SL2ℂ and our preceding works about SL3ℂ.