Abstract
Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights λ1,…,λr such that the tensor product VNλ1⊗⋯⊗VNλr contains nonzero G-invariants for some N⩾1, we show that the tensor product V2λ1⊗⋯⊗V2λr also contains nonzero G-invariants. This extends results of Kapovich–Millson and Belkale–Kumar and complements similar results for the general linear group due to Knutson–Tao and Derksen–Weyman. Our techniques involve the invariant theory of quivers equipped with an involution and the generic representation theory of certain quivers with relations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.