Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification the conjugacy classes unipotent elements $G(k)$ and nilpotent orbits on $\operatorname{Lie}(G)$ is well-established. One knows there are representatives every class as product root orbit sum elements. We give explicit in terms Chevalley basis for eminent classes. A (resp. nilpote...

We describe some of S.G.Dani’s many contributions to the theory and applications of dynamical systems on homogeneous spaces, with emphasis on unipotent flows. S.G.Dani has written over 100 papers. They explore a variety of topics, including: • flows on homogeneous spaces – unipotent dynamics – applications to Number Theory – divergent orbits – bounded orbits and Schmidt’s game – topological orb...

This paper continues the theme started in 1971 by G.A. Margulis [22] when he showed that trajectories of one-parameter unipotent flows on SL(k,R)/ SL(k,Z) are never divergent. This was earlier conjectured by I. Piatetski-Shapiro, and was used by Margulis for the proof of the Arithmeticity Theorem for non-uniform lattices. A decade later, S. G. Dani [7, 8, 10] modified the method of Margulis, sh...

For an inclusion F < G < L of connected real algebraic groups such that F is epimorphic in G, we show that any closed F -invariant subset of L/3 is G-invariant, where 3 is a lattice in L. This is a topological analogue of a result due to S. Mozes, that any finite F -invariant measure on L/3 is G-invariant. This result is established by proving the following result. If in addition G is generated...

0.1. Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a reductive connected algebraic group over k. Let U be the variety of unipotent elements of G. The unipotent classes of G are the orbits of the conjugation action of G on U . The theory of Dynkin and Kostant [Ko] provides a classification of unipotent classes of G assuming that p = 1. It is known that this cl...

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup of a split reductive group and show how this improves computation in the reductive group itself.

This is an extended version of the talk given by the first author at the conference. We report on the outcome of some experiments with the decomposition of products of (generalized) characters of some classical groups. In particular some results of the PhD-thesis of Dirk Mattig on the products of unipotent characters of general linear groups are presented and commented. In order to obtain simil...

This paper describes how to use subgroups to parameterize unipotent classes in the classical algebraic group in characteristic 2. These results can be viewed as an extension of the Bala-Carter Theorem, and give a convenient way to compare unipotent classes in a group G with unipotent classes of a subgroup X where G is exceptional and X is a Levi subgroup of classical type. AMS subject: 14L35, 2...

The finite generation of the ring of invariants of a special class of unipotent groups is established-namely, unipotent radicals of parabolic subgroups.

We study a class of double coset spaces RA\G1 × G2/RC , where G1 and G2 are connected reductive algebraic groups, and RA and RC are certain spherical subgroups of G1×G2 obtained by “identifying” Levi factors of parabolic subgroups in G1 and G2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin–Dri...