Translation-invariant line bundles on linear algebraic groups

Representations of Algebraic Groups and Principal Bundles on Algebraic Varieties

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic p. We quickly review the notions of stable and semistable vector bundles and principal G-bundles , where G is any semisimple group. We define the notion of a low height representation in characteristic p and outline a proof of the theorem t...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Translation-invariant Function Algebras on Compact Groups

Let X be a compact group. $(X) denotes the Banach algebra (point multiplication, sup norm) of continuous complexvalued functions on X A is any closed subalgebra of d(X) which is stable under right and left translations and contains the constants. It is shown, by means of the Peter-Weyl Theorem and some multilinear algebra, that the condition (*) every representation of degree 1 of X has finite ...

Translation-invariant linear operators

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...

Linear Algebraic Groups