TY - BOOK AU - Berman,Stephen AU - Parshall,Brian AU - Scott,Leonard AU - Wang,Weiqiang TI - Infinite-Dimensional Aspects of Representation Theory and Applications T2 - Contemporary Mathematics SN - 9780821879825 AV - QA176 -- .I58 2004eb U1 - 512 PY - 2005/// CY - Providence PB - American Mathematical Society KW - Representations of algebras -- Congresses KW - Representations of groups -- Congresses KW - Geometry, Algebraic -- Congresses KW - Algebra, Homological -- Congresses KW - Quantum groups -- Congresses KW - Electronic books N1 - Intro -- Contents -- Modular representation theory of Hecke algebras, a survey -- An application of free Lie algebras to polynomial current algebras and their representation theory -- Canonical basic sets for Hecke algebras -- On Universal Central Extensions of sln(A) -- Pseudoderivations, pseudoautomorphisms and simple current modules for vertex algebras -- Hilbert scheme intersection numbers, Hurwitz numbers, and Gromov-Witten invariants -- On Demazure crystals for Uq(D(3)4) -- Populations of solutions of the X X X Bethe equations associated to Kac-Moody algebras -- Representations of rational Cherednik algebras -- 1. Introduction -- 2. A motivation via Dunkl operators -- 2.1. Dimension 1 -- 2.2. Dimension n -- 3. Structure -- 3.1. The rational Cherednik algebra -- 3.2. The spherical subalgebra -- 4. Representation theory at t ≠ 0 -- 4.1. Category O -- 4.2. Dunkl operators and KZ functor -- 4.3. Primitive ideals and supports -- 4.4. Harish-Chandra bimodules -- 5. Representation theory at t = 0 -- 5.1. General representations -- 5.2. 0-fiber -- 6. Type A -- 6.1. Structure -- 6.2. Category o -- 6.3. Shift functors -- 6.4. Hilbert schemes -- 7. Type A1 -- 7.1. Presentation -- 7.2. Category 0 and KZ -- 7.3. Spherical subalgebra -- 7.4. Double affine Hecke algebra -- 8. Generalizations -- 8.1. Complex and symplectic reflection groups -- 8.2. Characteristic p > -- 0 -- 9. Table of analogies -- References -- A geometric construction of crystal graphs using quiver varieties: extension to the non-simply laced case UR - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113186 ER -