Irreducible modules over finite simple Lie conformal superalgebras of type K

Abstract

Abstract. We construct all finite irreducible modules over Lie conformal superalgebras of type K

Classification of finite irreducible conformal modules over Lie conformal superalgebras of Block type

“…(2) If p = −1, then, up to parity change, M is isomorphic to V (1) ∆,α or V (2) ∆,α for some ∆, α ∈ C with ∆ = 0, or V ∆,Λ,α,β for some ∆, Λ, α, β ∈ C with (2∆ ± Λ, β) = (0, 0).…”

“…0 (∂, 0) is independent of the variable ∂, which contradicts to the assumption deg e (2) 0 (∂, 0) = n ≥ 1. Thus, n = 0.…”

“…0 , as in Lemma 4.8, we must have that e (2) 0 (∂, λ) is independent of the variable ∂. In particular, e…”

“…λ) = 0. Hence, the action of J k on v(2) 0 has the required form. Next, we show that J k λ v(2) 1 = 0.…”

An upper bound on the degree of singular vectors for $E(1,6)$

“…The classification of all finite irreducible modules over the conformal superalgebras S 2,0 , K N , for N = 2, 3, 4 was obtained in [10]. Boyallian, Kac, Liberati and Rudakov classified all finite irreducible modules over the conformal superalgebras of type W and S in [4]; Boyallian, Kac and Liberati classified all finite irreducible modules over the conformal superalgebras of type K N for N ≥ 4 in [2]. All finite irreducible modules over the conformal superalgebra K ′ 4 were classified in [1].…”