Topics in Hidden Symmetries

Abstract

These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples related to the Lie algebra sl(2,C). Such consideration maybe regarded as toy one for analogous infinite dimensional problems in the modern quantum field theory (conformal field theory, integrable models, field theory in non-trivial backgrounds). Some constructions inspired by these topics and related to infinite dimensional hidden symmetries, which are produced by vertex operator fields, will be discussed in the forthcoming article.

11 pages AMSTEX, amsppt style

References in corpus (3)

• Infinite dimensional geometry and quantum field theory of strings. III. Infinite dimensional W-geometry of a second quantized free string
• Infinite Dimensional Geometry and Quantum Field Theory of Strings. II. Infinite Dimensional Noncommutative Geometry of a Self-Interacting String Field
• Setting Hidden Symmetries Free by the Noncommutative Veronese Mapping

Cited by in corpus (10)

• Approximate representations and Virasoro algebra
• Extending Representations of sl(2) to Witt and Virasoro algebras
• Droems: experimental mathematics, informatics and infinite dimensional geometry
• Hidden symmetries and categorical representation theory
• On the infinite-dimensional hidden symmetries. III. $q_R$-conformal symmetries at $q_R\to \infty$ and Berezin-Karasev-Maslov asymptotic quantization of $C^{\infty }(S^1)$
• On the infinite dimensional hidden symmetries. I. Infinite dimensional geometry of $q_R$-conformal symmetries
• Isotopic pairs and their representations. II. A general supercase
• Infinite dimensional geometry of $M_1=Dif{f}_{+}(S^1)/PSL(2,R)$ and $q_R$-conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra
• Cross-projective representations of pairs of anticommutative algebras, alloys and finite-dimensional irreducible representations of some infinite-dimensional Lie algebras
• q_R-conformal symmetries in 2D nonlocal quantum field theory, categorical representation theory, and Virasoro algebra