ATTENTION, EXCEPTIONNELLEMENT, LE SÉMINAIRE AURA LIEU EN SALLE 125 !
(exposé en anglais) Let V be a bi-graded vector space. We consider graded nilpotent pairs of V up to Levi-base change, that is, base change which respects the bi-grading of V. Our main goal in this talk is to prove and approach certain finiteness conditions. In order to do so, we define a class of finite-dimensional algebras, the so-called «Staircase algebras» parametrized by Young diagrams. We develop a complete classification of representation types of these algebras and look into finite, tame (concealed) and wild cases briefly. Furthermore, we discuss possible generalizations and translate all results to the setup of graded nilpotent pairs in order to get the mentioned finiteness criteria.
