The Bott–Borel–Weil Theorem for direct limit groups
The Bott–Borel–Weil Theorem for direct limit groups
We show how highest weight representations of certain infinite dimensional Lie groups can be realized on cohomology spaces of holomorphic vector bundles. This extends the classical Bott–Borel–Weil Theorem for finite–dimensional compact and complex Lie groups. Our approach is geometric in nature, in the spirit of Bott's original generalization of the …