Connection matrices on the Siegel-Jacobi upper half space and extended Siegel-Jacobi upper half space

2024/07/05 by Elena Mirela Babalic, Babalic, Elena Mirela, Stefan Berceanu +1
Mathematics · #37J55 #53C05 #53D15 #81Q70 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.04310

openalex publication_date 2024/07/05 · openalex created_date 2024/07/09 · openalex updated_date 2026/07/28

Abstract

The inverse of the metric matrices on the Siegel-Jacobi upper half space X^J_n, invariant to the restricted real Jacobi group G^J_n(ℝ)₀ and extended Siegel-Jacobi X^J_n upper half space, invariant to the action of the real Jacobi G^J_n(ℝ), are presented. The results are relevant for Berezin quantization of the manifolds X^J_ n and X^J_n. Explicit calculations in the case n=2 are given.

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