Absolutely indecomposable quasi-parabolic $G$-bundles and the multiplicity of irreducible characters

Abstract

Absolutely indecomposable vector bundle and parabolic vector bundles are well-studied via quiver representations. In this paper, we study absolutely indecomposable quasi-parabolic $G$-bundles over ${\mathbb{P}}^1$ with generic additive character varieties. Furthermore, we give a geometric interpretation of the multiplicity of the tensor product of irreducible characters of finite reductive groups using generic additive character varieties.

Minor corrections, and the formula for the number of absolutely indecomposable quasi-parabolic $G$-bundles is added