On the saturation conjecture for Spin(2n)

2018/04/24 by Joshua Kiers, Kiers, Joshua
Mathematics · #14L24 #14M15 #22E46 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.09229

openalex publication_date 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type D (the even spin groups: Spin(2n) for n≥ 4 an integer), extending work done by Kumar-Kapovich-Millson on Spin(8). Our main theorem asserts that the saturation conjecture holds for Spin(10) and Spin(12): for all triples of dominants weights λ,μ,ν such that λ+μ+ν is in the root lattice, and for any N>0, (V(λ)⊗ V(μ)⊗ V(ν))^G ≠ 0 if and only if (V(Nλ)⊗ V(Nμ)⊗ V(Nν))^G≠ 0, for G= Spin(10) or Spin(12). Some related results for groups of other types are listed as well.

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