Kac–Moody Superalgebras and Integrability

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Dualities and Representations of Lie Superalgebras (2012, background): “, [Sva2]), and more generally for Kac-Moody Lie superalgebras in Kac-Wakimoto [KW, Lemma 1.”
On finite-dimensional Hopf algebras (2014, background): “he root system of g(A,p). We make the following technical assumptions: ajk = 0 =⇒ akj = 0, j 6= k; (3.12) adfi is locally nilpotent in g(A,p), i ∈ I. (3.13) The matrix A is admissible if (3.13) holds [80]. Let CA,p = (cA,p ij )i,j∈I be given by cA,p ij := −min{m ∈ N0 : (adfi)m+1fj = 0},i 6= j ∈ I, c”
Representations of Lie superalgebras in prime characteristic I (2008, background): “(see [16] for the basic properties of odd reflections).”
Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras (2009, unknown): “ (λ+ρ,γ) = 0. Proof. - For an arbitrary Borel subalgebra b′ containing b0 let λ(b′) denote the highest weight of Lλ with respect to b′ and ρ(b′) be the analogue of ρfor b′. A weight λis dominant (see [27]) if for any simple root αof b0 there exists a Borel subalgebra b′ such that αor α 2 is simple i”