Algebra Seminar: Odd reflections and super category O

Abstract: The classification of basic classical Lie superalgebras due to Kac may nowadays be viewed as being almost embedded into the classification of Nichols algebras of diagonal type by Weyl groupoids (a.k.a. generalized root systems in the sense of Heckenberger–Yamane). Weyl groupoids naturally generalizes classical root systems by allowing essentially different choices of bases. From this perspective, the existence of essentially different choices of Borel subalgebras in Lie superalgebras, as well as the notion of odd reflections, appears to be fundamentally important, and their representation-theoretic manifestations are of particular interest. In this talk, I will present some of the most elementary properties concerning category 𝒪 of basic classical Lie superalgebras from this point of view, and also discuss the finiteness/infinitenss of projective dimensions of Verma supermodules.

The seminar will be held via Zoom link (meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.