Title Lie Algebras, Vertex Operator Algebras, and Related Topics

Published Providence : American Mathematical Society, 2017

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Description 1 online resource (282 pages) Series Contemporary Mathematics ; v. 695 Contemporary Mathematics Contents Cover; Title page; Contents; Preface; Generalizations of -systems and orthogonal polynomials from representation theory; 1. Introduction; 2. Calculating ̂ ₂ Tau-Functions on Two-Component Fermionic Fock Space; 3. Generalizing to ̂ ₃; 4. Connection Matrices and Zero Curvature Equations; 5. Orthogonal Polynomials from Connection Matrices; References; Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory; 1. Introduction; 2. Classification of irreducible modules for orbifold \triplet̂{ _{ }}: A fusion rules approach 3. Fusion rules for \singlet and a proof of Conjecture 2.3 for =2.4. Deformed realization of the triplet and singlet vertex algebra; 5. Intertwining operators between typical \singlet and \triplet̂{ _{ }}-modules: the =2 case; Acknowledgments; References; Kac-Moody groups and automorphic forms in low dimensional supergravity theories; 1. Introduction; 2. Supergravity theories; 3. Construction of Kac-Moody groups over \R and \Z; 4. Eisenstein series in supergravity; 5. Eisenstein series on non-affine Kac-Moody groups; 6. Some open questions; References The Lusztig-Macdonald-Wall polynomial conjectures and -difference equations1. Introduction and statement of results; 2. Hypergeometric -series and proofs of results; 3. The LMW polynomials and the affine Lie algebra ̂\frak{ }₂; References; Uniqueness of representation-theoretic hyperbolic Kac-Moody groups over $! 1. Introduction; 2. Tits' Kac-Moody group; 3. Tits' presentation; 4. Simply laced hyperbolic type; 5. Finitely many defining relations parametrized over ; 6. Representation-theoretic Kac-Moody groups over rings 7. Uniqueness of representation-theoretic Kac-Moody groups over \Z8. The kernel of _{ }; Acknowledgement; References; Coends in conformal field theory; 1. Coends in mathematics and physics; 2. Some facts about specific coends; 3. Coends in functor categories; 4. Fubini theorems; References; Remarks on -coordinated modules for quantum vertex algebras; 1. Introduction; 2.-coordinated modules for weak quantum vertex algebras; 3.-coordinated module ((), _{ }*); References; The classification of chiral WZW models by ⁴?(B(, $!; 1. Introduction; 2. Geometric quantization 3. ⁴() for connected Lie groups4. Representations of affine and Heisenberg VOAs; 5. Simple current extensions; 6. The minimal energy; 7. The classification of chiral WZW models; 8. WZW conformal nets; 9. Conclusion; References; Some open problems in mathematical two-dimensional conformal field theory; 1. Introduction; 2. The construction of rational conformal field theories satisfying the axioms of Kontsevich-Segal-Moore-Seiberg; 3. Cohomology theory for graded vertex algebras and complete reducibility of their modules; 4. The moduli space of conformal field theories Summary This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14-18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, Notes 5. The construction and study of logarithmic conformal field theories Print version record Subject Lepowsky, J. (James) Wilson, Robert L., 1946- Wilson, Robert L., 1946- Lepowsky, J. (James) Lie algebras -- Congresses Vertex operator algebras -- Congresses Representations of algebras -- Congresses Lie algebras Representations of algebras Vertex operator algebras Genre/Form Conference papers and proceedings Form Electronic book Author Jurisich, Elizabeth Milas, Antun ISBN 9781470441968 1470441969

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