Galois ...-factors modulo roots of unity.
The spectrum of a Gelfand pair , where is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz -invariant functions on . We also show the converse in the case of the Gelfand pair , where is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.
We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
We generalize Jacobi forms of an arbitrary degree and construct torus bundles over abelian schemes whose sections can be identified with such generalized Jacobi forms.
In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.