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

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 $sl(2,C)$ is found. The analysis and the unraveling of the algebraic structure of these families of hidden symmetries are performed.