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Logarithmic CFTs connected with simple Lie algebras
Boris Feigin,I. Yu. Tipunin +1 more
TL;DR: For any root system corresponding to a semisimple simply-laced Lie algebra, a logarithmic CFT is constructed as discussed by the authors, where characters of irreducible representations are calculated in terms of theta functions.
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Abstract: For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
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On the Feigin-Tipunin conjecture
TL;DR: In this paper, the authors proved the Feigin-Tipunin conjecture on the geometric construction of logarithmic W-algebras associated to a simple Lie algebra and integer p bigger than 2, and their modules.
Quantum groups and Nichols algebras acting on conformal field theories
TL;DR: In this article, it was shown that certain screening operators in conformal field theory obey algebra relations of a corresponding Nichols algebra with diagonal braiding, by proving an analytical quantum symmetrizer formula for the functions.
Vertex operator (super)algebras and LCFT
Dražen Adamović,Antun Milas +1 more
TL;DR: In this paper, a review of the developments in logarithmic conformal field theory from the vertex algebra point of view is presented, focusing on vertex operator (super) algebras of the triplet type.
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Higher rank partial and false theta functions and representation theory
Thomas Creutzig,Antun Milas +1 more
TL;DR: In this article, higher rank Jacobi partial and false theta functions associated to positive definite rational lattices (ADE root lattices) are studied and modulo conjecture properties of regularized Kostant's partial functions are derived for (1,p)-singlet W-algebras.
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Higher depth quantum modular forms, multiple Eichler integrals, and $\frak{sl}_3$ false theta functions.
TL;DR: In this paper, the authors introduced and studied higher depth quantum modular forms of positive integral weight, and proved that the false theta of the vertex algebra W^0(p)_{A_2} can be expressed as the sum of two depth two quantum modular functions of positive weight.
References
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Infinite-dimensional Lie algebras
Ralph K. Amayo,Ian Stewart +1 more
- 31 Oct 1974
TL;DR: In this article, the authors consider a class of Lie algebras in which every subalgebra is a subideal, and they show that it is possible to construct a locally coalescent class of these classes.
3.3K
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Vertex algebras for beginners
Victor G. Kac
- 01 Jan 1997
TL;DR: In this paper, a formal distribution a(z,w) = 2 QFT and chiral algebras is defined and the Virasoro algebra is defined, which is a generalization of the Wightman axioms.
1.7K
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Vertex Algebras and Algebraic Curves
Edward Frenkel,David Ben-Zvi +1 more
- 01 Jan 2000
TL;DR: Vertex algebra bundles are associated with Lie algebras and operator product expansion (OPE) as mentioned in this paper, and vertex algebra bundles can be used to represent internal symmetries of vertex algebra.
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Vertex Algebras and Algebraic Curves
Abstract: Introduction Definition of vertex algebras Vertex algebras associated to Lie algebras Associativity and operator product expansion Applications of the operator product expansion Modules over vertex algebras and more examples Vertex algebra bundles Action of internal symmetries Vertex algebra bundles: Examples Conformal blocks I Conformal blocks II Free field realization I Free field realization II The Knizhnik-Zamolodchikov equations Solving the KZ equations Quantum Drinfeld-Sokolov reduction and $\mathcal{W}$-algebras Vertex Lie algebras and classical limits Vertex algebras and moduli spaces I Vertex algebras and moduli spaces II Chiral algebras Factorization Appendix Bibliography Index List of frequently used notation.
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