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 Tata Institute of Fundamental Research 2006; 535 pp; hardcover ISBN-10: 81-7319-802-0 ISBN-13: 978-81-7319-802-1 List Price: US$50 Member Price: US$40 Order Code: TIFR/11 The area of algebraic groups and homogeneous spaces is one in which major advances have been made in recent decades. This was the theme of the (twelfth) International Colloquium organized by the Tata Institute of Fundamental Research in January 2004, and this volume constitutes the proceedings of that meeting. This volume contains articles by several leading experts in central topics in the area, including 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 the 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. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. Table of Contents T. A. Springer -- Armand Borel's work in the theory of linear algebraic Groups H. H. Andersen -- Cohomology of Line Bundles P. Belkale -- Extremal unitary local systems on $$\mathbb{P}^1-\{p_1,\ldots,p_s\}$$ I. Biswas and T. L. Gómez -- Higgs fields and flat connections on a principal bundle over a compact Kähler manifold M. Brion -- Construction of equivariant vector bundles J.-L. Colliot-Thélène and J.-J. Sansuc -- The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group) C. De Concini and C. Procesi -- On the geometry of graph arrangements P. Deligne -- La catégorie des représentations du groupe symétrique $$S_t$$, lorsque $$t$$ n'est pas un entier naturel H. Garland -- Eisenstein series on loop groups: Maass-Selberg relations 1 W. van der Kallen -- A reductive group with finitely generated cohomology algebras S. S. Kannan -- Cohomology of line bundles on Schubert varieties in the Kac-Moody setting F. Knop -- Composition Kostka functions V. Kreiman, V. Lakshmibai, P. Magyar, and J. Weyman -- On ideal generators for affine Schubert varieties H. Nakajima -- Crystal, canonical and PBW bases of quantum affine algebras R. Orellana and A. Ram -- Affine braids, Markov traces and the category $$\mathcal{O}$$ R. Parthasarathy -- Quantum analogues of a coherent family of modules at roots of One: $$\mathfrak{g}_2$$ V. L. Popov -- Generically multiple transitive algebraic group actions T. A. Springer -- Some subvarieties of a group compactification