Infinite-Dimensional Aspects of Representation Theory and Applications.

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 &gt -- 0 -- 9. Table of analogies -- References -- A geometric construction of crystal graphs using quiver varieties: extension to the non-simply laced case.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.