Abstract: Motivated by the ubiquity of determinantal structures in the mathematical physics literature, e.g. random matrices, statistical mechanics models, we propose to revisit and extend the seminal construction of Karlin-McGregor by developing a theory of C0-semigroups (non-necessarily Markovian) on the Weyl Chamber W(E). We take an operator theoretical approach and use the following three ideas : 1) a lifting procedure from E to W(E), 2) some classical and more recently introduced isospectral classifications schemes, 3) another view of semigroups on W(E) than the determinantal one. We illustrate our approach with some examples such as dynamical versions of the LUE ensemble and continuous and discrete Borodin-Muttalib biorthogonal ensembles and their Boson analogues.

Joint work with Pierre Patie.