• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.627-647
• /
• 2015

In this paper, we construct the Schr$\ddot{o}$dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m and find covariant maps for the Schr$\ddot{o}$dinger-Weil representation.

• Journal of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.409-425
• /
• 2024

The category of pairs is the category whose objects are maps between two based spaces and morphisms are pair-maps from one object to another object. To study the self-homotopy equivalences in the category of pairs, we use covariant functors from the category of pairs to the group category whose objects are groups and morphisms are group homomorphisms. We introduce specific subgroups of groups of self-pair homotopy equivalences and put these groups together into certain sequences. We investigate properties of these sequences, in particular, the exactness and split. We apply the results to two special functors, homotopy and homology functors and determine the suggested several subgroups of groups of self-pair homotopy equivalences.