Invariants of equivariant algebraic vector bundles and inequalities for dominant weights (Q1373500)

It is well known that all algebraic vector bundles over an affine complex space are trivial. In this article the authors are concerned with the equivariant setting. \textit{G. W. Schwarz} [C. R. Acad. Sci. Paris, Sér. I 309, No. 2, 89-94 (1989; Zbl 0688.14040)], has shown that in this setting equivariant vector bundles over representations need not be trivial when the base representation has a one dimensional quotient. The authors construct many large families of distinct equivariant bundles with a fixed base representation (not necessarily having one-dimensional quotient) and fixed fiber representation. In order to do so they use the structure of weights of groups.