Components of $V(\rho )\otimes V(\rho )$ and dominant weight polyhedra for affine Kac-Moody Lie algebras

Sam Jeralds, Shrawan Kumar

Kostant asked the following question: Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers. Let $\lambda$ be a dominant integral weight. Then, $V(\lambda )$ is a component of $V(…