Tata Institute of Fundamental Research 2006; 535 pp; hardcover ISBN10: 8173198020 ISBN13: 9788173198021 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 KacMoody 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. ColliotThélène 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: MaassSelberg 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 KacMoody 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
