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We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different loc...
We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [E. Sommers, Comm. Math. Univ. Sancti Pauli ...
For the classical groups, Kraft and Procesi have resolved the question of which nilpotent orbits have closures that are normal and which do not, with the exception of the very even orbits in D2l that ...
We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and Kato's exotic nilpotent cone. We prove that the number of $\F_q$-points in each nilpotent orbit of type $B_n$ or $C_n$ eq...
The Lindeberg theorem is derived on stratilied nilpotent Lie groups; that is a normal convergence theorem for a triangular system of probability measures in case of bounded (homogemous) moments of ...
The Strong Law of Large Numbers due to Marcinkiewicz and Zygmund is carried over to simply connected step 2-nilpotent Lie groups. Moreover, for such groups, we prove analogues of the classical theo...

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