Shrinking targets for semisimple groups

Livšic’s theorem for semisimple Lie groups

In this paper we show that strong generalizations of the measurable Livšic theorem for cocycles taking values in connected non-compact linear semisimple Lie groups, a canonical example being SL(2,R), can be deduced from an elegant approach of Brin and Pesin to the dynamics of partially hyperbolic systems.

Shrinking Targets for Regularization of Logistic Regression

A Polytope Calculus for Semisimple Groups

We define a collection of polytopes associated to a semisimple group G. Weight multiplicities and tensor product multiplicities may be computed as the number of such polytopes fitting in a certain region. The polytopes are defined as moment map images of algebraic cycles discovered by I. Mirković and K. Vilonen. These cycles are a canonical basis for the intersection homology of (the closures o...

Heinz-Kato’s inequalities for semisimple Lie groups

Extensions of Heinz-Kato’s inequalities and related inequalities are obtained for semisimple connected noncompact Lie groups. Mathematics Subject Index 2000: Primary 22E46; Secondary 15A45

Representations of Semisimple Lie Groups

Let G be a Lie group and § a Banach space. A representation n of G on § is a mapping which assigns to every element x in G a bounded linear operator n(x) on § such that the following two conditions are fulfilled: (1) 7t(xy) = n(x) 7i(y) (x, y e G),n(l) = / and (2) the mapping (x, tp) ->uz(x)y) of G x § into § is continuous. (Here 1 is the unit element of G and I is the unit operator,) In partic...