By Michel Brion (auth.), Abraham Broer, A. Daigneault, Gert Sabidussi (eds.)

The 12 lectures offered in *Representation Theories and Algebraic**Geometry* specialize in the very wealthy and strong interaction among algebraic geometry and the illustration theories of varied sleek mathematical buildings, comparable to reductive teams, quantum teams, Hecke algebras, limited Lie algebras, and their partners. This interaction has been generally exploited in the course of contemporary years, leading to nice development in those illustration theories. Conversely, a very good stimulus has been given to the advance of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.

the diversity of issues lined is broad, from equivariant Chow teams, decomposition periods and Schubert types, multiplicity loose activities, convolution algebras, ordinary monomial idea, and canonical bases, to annihilators of quantum Verma modules, modular illustration thought of Lie algebras and combinatorics of illustration different types of Harish-Chandra modules.