Lie algebra automorphisms, the Weyl group, and tables of shift vectors

DOI10.1063/1.528422zbMath0668.17011OpenAlexW2091601977WikidataQ115331825 ScholiaQ115331825MaRDI QIDQ3820759

Peter Bouwknegt

Publication date: 1989

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528422

zbMATH Keywords

tablesalgorithmWeyl groupautomorphism grouporbifoldmoduli spacesimply laced Lie algebrasWess-Zumino-Witten modelstring models2-D conformal field theoriesgeneralized theta function identitiesshift vectors

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40)

Related Items

Towards a non-Abelian electric-magnetic symmetry: The skeleton group, Hurwitz numbers for reflection groups. II: Parabolic quasi-Coxeter elements, MORE ABOUT ALL CURRENT-ALGEBRAIC ORBIFOLDS, On asymmetric orbifolds and the \(D=5\) no-modulus supergravity, Lattices and strings, On a normal ordering ambiguity in the twisted WZW model

Cites Work

• Infinite-dimensional Lie algebras, theta functions and modular forms
• \(c=I\) conformal field theories on Riemann surfaces
• Modular and conformal invariance constraints in representation theory of affine algebras
• Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants
• An elucidation of Infinite-dimensional algebras\dots and the very strange formula. \(E^{(1)}_8\) and the cube root of the modular invariant j
• Basic representations of affine Lie algebras and dual resonance models
• Unitary representations of some infinite dimensional groups
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• Automorphisms of finite order of semisimple Lie algebras
• Semisimple subalgebras of semisimple Lie algebras
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Calculus of twisted vertex operators
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS