Representations of finite dimensional algebras and related topics in Lie theory and geometry

There has been no exposition of group representations and harmonic analysis suitable for graduate students for over twenty years. In this, the first of two projected volumes, the authors remedy the situation by surveying all the basic theory developed since the pioneering work of Kirillov in 1958, and consolidating more recent results. Topics covered include basic Kirillov theory, algorithms for parametrizing all coadjoint orbits. The authors have not only given here a modern account of all topics necessary for current research, but have also included many computed examples. This volume can serve then either as a handbook for specialists, with a complete, self-contained exposition of major results, or as a textbook suitable for graduate courses in harmonic analysis Semigroup and Ring Theoretical Methods in Probability / Kenneth S. Brown -- Typical Examples of Tame Algebras / Thomas Bruestle -- Representation Dimension and Solomon Zeta Function / Osamu Iyama -- Filtrations, Stratifications and Applications / Steffen Koenig -- Bruhat-Renner Decomposition and Hecke Algebras of Reductive Monoids / Mohan S. Putcha -- Representations and Blocks of Algebraic Monoids / Lex E. Renner -- The Descent Algebra of the Symmetric Group / Manfred Schocker -- A Remark on Letzter-Makar-Limanov Invariants / Yuriy Berest -- Derived Categories of Coherent Sheaves on Rational Singular Curves / Igor Burban -- Vector Bundles and Cohen -- Macaulay Modules / Yuriy A. Drozd