## Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional MethodsProceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general |

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### Contents

1 | |

Quantum and infinitedimensional methods 2 Crystal bases | 135 |

Quantum and infinitedimensional methods 3 Quantum groups and category theory | 177 |

Quantum and infinitedimensional methods 4 Vertex operator algebras the moonshine module and related topics | 261 |

Quantum and infinitedimensional methods 5 Infinite dimensional groups and Lie algebras | 349 |

### Common terms and phrases

2-category 2-morphism 2-vector abelian intertwining algebra algebraic groups associated axiom basis bialgebra binary trees braid group canonical CM(Z coefficients cohomology commutative conformal field theory consider construction coordinate algebra Corollary corresponding decomposition defined definition denote diagram direct limit direct sum elements example external nodes filtration finite dimensional function functor given Hence highest weight vector homogeneous homomorphism Hopf algebra hyperalgebra induced integrable irreducible isomorphism Jacobi identity Kac-Moody Lemma Lie algebra Lie group line bundles linear Lusztig Math Mathematics matrix monoidal category morphisms multiplication nonzero notation objects obtain permutation permutohedron polynomial polytope Proposition prove quantized enveloping algebras quantum groups rational relations representations resp root satisfies semi-infinite semijective structure subalgebra subspace tensor product topology U-module Vect vector space vertex algebra vertex operator algebra Virasoro algebra Yang-Baxter equation Zamolodchikov equations