Let G be a compact Lie group of type $$B_{n},$$ such as $$SO(2n+1)$$ . We characterize the tuples $$(x_{1},\ldots ,x_{L})$$ elements $$x_{j}\in G$$ which have property that product their conjugacy classes has non-empty interior. Equivalently, convolution orbital measures supported on is absolutely continuous with respect to Haar measure. The characterization depends dimensions largest eigenspac...
