## Infinite-Dimensional Aspects of Representation Theory and Applications: International Conference on Infinite-Dimensional Aspects of Representation Theory and Applications, May 18-22, 2004, University of Virginia, Charlottesville, VirginiaThe University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory. |

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### Contents

1 | |

An application of free Lie algebras to polynomial current algebras and their representation theory | 15 |

Canonical basic sets for Hecke algebras | 33 |

On Universal Central Extensions of slnA | 43 |

Pseudoderivations pseudoautomorphisms and simple current modules for vertex algebras | 55 |

Hilbert scheme intersection numbers Hurwitz numbers and GromovWitten invariants | 67 |

On Demazure crystals for UqD34 | 83 |

Populations of solutions of the X X X Bethe equations associated to KacMoody algebras | 95 |

Representations of rational Cherednik algebras | 103 |

extension to the nonsimply laced case | 133 |

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Infinite-dimensional Aspects of Representation Theory and Applications ... Stephen Berman No preview available - 2005 |

### Common terms and phrases

a-modules affine Hecke algebra affine Lie algebra algebra associated algebras of type associative algebra automorphism Bethe equation Bethe solutions canonical basic set central extension cohomology computation construction corresponding crystal base crystal graph decomposition map decomposition numbers defined definition deformation Demazure crystals denote double affine Hecke element End(V endomorphism equivariant EtGi Etingof Fock space functor Geck given Heisenberg highest weight Hilb Hilbert schemes homology HW q ideal integrable Irr(HK Irr(W irreducible components isomorphism Kac-Moody algebra Kac-Moody Lie algebra Kashiwara Lemma linear Lusztig's Math Mathematics Morita equivalence morphism Note partition perfect crystal polynomials PROOF Proposition pseudoderivation pseudoendomorphism quantum affine algebra quiver varieties quotient r-tuple rational Cherednik algebra representation theory resp schemes of points semi-simple set of irreducible simple modules structure subalgebra subset tensor product Theorem universal central extension universal enveloping algebra vector space vertex algebra Weyl group Young diagram