Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional 'instructional' workshop preceding the conference, there were also workshops on 'Commutative Algebra, Algebraic Geometry and Representation Theory', 'Finite Dimensional Algebras, Algebraic Groups and Lie Theory', and 'Quantum Groups and Hall Algebras'. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated.The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented.The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

Table of Contents:
Instructional Workshop: Semigroup and ring theoretical methods in probability by K. S. Brown Typical examples of tame algebras by T. Bruestle Representation dimension and Solomon zeta function by O. Iyama Filtrations, stratifications and applications by S. Koenig Bruhat-Renner decomposition and Hecke algebras of reductive monoids by M. S. Putcha Representations and blocks of algebraic monoids by L. E. Renner The descent algebra of the symmetric group by M. Schocker Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory: A remark on Letzter-Makar-Limanov invariants by Y. Berest Derived categories of coherent sheaves on rational singular curves by I. Burban Vector bundles and Cohen-Macaulay modules by Y. A. Drozd Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory: Finite dimensional algebras, quantum groups and finite groups of Lie type by J. Du Stratified algebras arising in Lie theory by V. Mazorchuk Character formulas of Kazhdan-Lusztig type by T. Tanisaki Weight theory in the context of arbitrary finite groups by P. Webb Specialized Workshop Quantum Groups and Hall Algebras: Restricted two-parameter quantum groups by G. Benkart and S. Witherspoon On Ringel-Hall algebras by B. Deng and J. Xiao Lusztig's geometric approach to Hall algebras by Z. Lin The use of geometric and quantum group techniques for wild quivers by M. Reineke An introduction to perverse sheaves by K. Rietsch An introduction to canonical bases by Y. Saito Quivers of type $A$, flag varieties and representation theory by O. Schiffmann.