The Siegel upper half space is the generalization of the upper half-plane as one passes from the description of complex elliptic curves to that of Riemann surfaces of higher genus.
The Siegel upper half space of degree (or genus ) is the set of symmetric matrices whose entries are complex numbers with positive-definite imaginary part.
The Siegel upper half space of degree may be obtained as the quotient of the symplectic group by its maximal compact subgroup (and the stabilizer of ), the unitary group , embedded into as follows:
Last revised on November 23, 2022 at 04:58:26. See the history of this page for a list of all contributions to it.