1998/06/25 by Denis V. Juriev, Juriev, Denis V.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.DG #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/9806140
14 pp, AMSTEX
arxiv created 1998/06/25 · openalex publication_date 1998/06/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A geometric interpretation of approximate (HS-projective or TC-projective) representations of the Witt algebra wC by qR-conformal symmetries in the Verma modules Vh over the Lie algebra sl(2,C) is established and some their characteristics are calculated. It is shown that the generators of representations coincide with the Nomizu operators of holomorphic wC-invariant hermitean connections in the deformed holomorphic tangent bundles Th(M1) over the infinite-dimensional Kähler manifold M1=\Diff+(S1)/PSL(2,R), whereas the deviations AXY of the approximate representations coincide with the curvature operators for these connections, which supply the determinant bundle det Th(M1) by a structure of the prequantization bundle over M1. At h=2 the geometric picture reduces to one considered by A.A.Kirillov and the author [Funct.Anal.Appl. 21(4) (1987) 284-293] (without any relation to the approximate representations) for ordinary tangent bundles.