Category of Finite Dimensional Modules over an Orthosymplectic Lie Superalgebra: Small Rank Examples

Abstract

International audienceThe aim is to give a concrete picture of simple and projective finite dimensional modules over osp(5,4)

Bipartite extension graphs and the Duflo--Serganova functor

“…Let diag(L ′ ) be the diagonal copy of L ′ in (L ′ ) ⊕m and let N be the preimage of diag(L ′ ) in ⊕M i . This gives the exact sequence of the form (17) and the commutative diagram (18). Let us show that N is indecomposable.…”

“…Main results. The multiplicities i K λ,ν p (p) ,p (p−1) were computed by C. Gruson and V. Serganova in [17] (see [18] for small rank examples); we will recall their results in 4.5 below. These results imply that the graph Γ(χ) defined in 3.5 is N-graded and that dex defines a Z 2 -grading on Γ(χ).…”