Abstract
The Foulkes conjecture states that the multiplicities in the plethysm Syma(SymbV) are at most as large as the multiplicities in the plethysm Symb(SymaV) for all a≤b. This conjecture has been known to be true for a≤4. The main result of this paper is its verification for a=5. This is achieved by performing a combinatorial calculation on a computer and using a propagation theorem of Tom McKay from 2008.Moreover, we obtain a complete representation theoretic decomposition of the vanishing ideal of the 5th Chow variety in degree 5, we show that there are no degree 5 equations for the 6th Chow variety, and we also find some representation theoretic degree 6 equations for the 6th Chow variety.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
