We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique which we successfully applied in first calculations of lightest $Lambda$ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon-nucleon and nucleon-hyperon interactions (such as those derived from EFT). We discuss formal aspects of the methodology, show first demonstrative results for ${}_{Lambda}^3$H, ${}_{Lambda}^4$H and ${}^4_Lambda$He, and give outlook.
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