Infinite dimensional geometry of $M_1=Diff_+(S^1)/PSL(2,R)$ and $q_R$-conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra

Denis V. Juriev

paper

Infinite dimensional geometry of $M_{1} = D i f f_{+} (S^{1}) / P S L (2, R)$ and $q_{R}$ -conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra

arXiv:math/9807142

Abstract

Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via $q_{R}$ -conformal symmetries in the Verma modules over the Lie algebra $s l (2, C)$ is found. The analysis and the unraveling of the algebraic structure of these families of hidden symmetries are performed.

15 pp, AMSTEX: 1st part - math.RT/9806140

Infinite dimensional geometry of M1​=Diff+​(S1)/PSL(2,R) and qR​-conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra

Abstract

Infinite dimensional geometry of $M_{1} = D i f f_{+} (S^{1}) / P S L (2, R)$ and $q_{R}$ -conformal symmetries. II. Geometric quantization and hidden symmetries of Verma modules over Virasoro algebra