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

Abstract

After introducing the generators and irreducible representations of the $\mathrm{su}(5)$ and $\mathrm{so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces $\mathrm{su}(5)/\mathrm{su}(4)\times \mathrm{u}(1)$ and $\mathrm{so}(6)/\mathrm{so}(4)\times \mathrm{so}(2)$ are derived in terms of the diagonal subalgebras $\mathrm{su}(4)\times \mathrm{u}(1)$ and $\mathrm{so}(4)\times \mathrm{so}(2)$, respectively.

13 pages. Typos corrected