Major advances have been made in the area of Algebraic Groups and Homogeneous Spaces in recent decades. This volume contains articles by several leading experts in central topics in the area, including representation theory in characteristic p, combinatorial representation theory, flag varieties, Schubert varieties, vector bundles, loop groups and Kac-Moody Lie algebras, Galois cohomology of algebraic groups, and Tannakian categories. In addition to original papers in these areas, the volume includes a survey on representation theory in characteristic p by H. Andersen and an article by T.A. Springer on Armand Borel’s work in algebraic groups and Lie groups.

Armand Borel’s Work in the Theory of Linear Algebraic Groups / Cohomology of Line Bundles / Extremal Unitary Local Systems on P1 – {p1,…,ps}/ Higgs Fields and Flat Connections on a Principal Bundle Over a Compact Kähler Manifold / Construction of Equivariant Vector Bundles / The Rationality Problem for Fields of Invariants Under Linear Algebraic Groups (With Special Regards to the Brauer Group) / On the Geometry of Graph Arrangements / La Catégorie des Représentations du Groupe Symétrique St, Lorsque t n’est pas un Entier Naturel / Eisenstein Series on Loop Groups: Maass-Selberg Relations 1 / A Reductive Group with Finitely Generated Cohomology Algebras / Cohomology of Line Bundles on Schubert Varieties in the Kac-Moody Setting / Composition Kostka Functions / On Ideal Generators for Affine Schubert Varieties / Crystal, Canonical and PBW Bases of Quantum Affine Algebras / Quantum Analogues of a Coherent Family of Modules at Roots of One: g2 / Generically Multiple Transitive Algebraic Group Actions / Some Subvarieties of a Group Compactification.

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