Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rmsu}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators,the general kernel solutions of the Kostant operators on eight-dimensionalquotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rmso}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonalsubalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$,respectively.Comment: 13 pages. Typos correcte