The multiplicity of weights in nonprimitive pairs of weights
Abstract
Description
For each type of classical Lie algebra, we list the dominant highest weights $ζ$ for which $(ζ;μ_i)$ is not a primitive pair and the weight space $V_{μ_i}$ has dimension one where $μ_i$ are the highest long and short roots in each case. These dimension one weight spaces lead to examples of nilmanifolds for which we cannot prove or disprove the density of closed geodesics.
25 pages
25 pages