Denominator Identity for Affine Lie Superalgebras with Zero Dual Coxeter Number
نویسندگان
چکیده
0.1. Let g be a complex finite-dimensional contragredient Lie superalgebra. These algebras were classified by V. Kac in [K1] and the list (excluding Lie algebras) consists of four series: A(m|n), B(m|n), C(m), D(m|n) and the exceptional algebrasD(2, 1, a), F (4), G(3). The finite-dimensional contragredient Lie superalgebras with zero Killing form (or, equivalently, with dual Coxeter number equal to zero) are A(n|n), D(n|n+ 1) and D(2, 1, a).
منابع مشابه
Weyl Denominator Identity for Affine Lie Superalgebras with Non-zero Dual Coxeter Number
Weyl denominator identity for the affinization of a basic Lie superalgebra with non-zero Killing form was formulated by V. Kac and M. Wakimoto and was proven by them for the defect one case. In this paper we prove this identity. 0. Introduction Let g be a basic Lie superalgebra with a non-zero Killing form. Let ĝ be the affinization of g. Let h (resp., ĥ) be the Cartan subalgebra in g (resp., i...
متن کاملWeyl Denominator Identity for Finite-dimensional Lie Superalgebras
Weyl denominator identity for finite-dimensional Lie superalgebras conjectured by V. Kac and M. Wakimoto is proven.
متن کاملMonstrous Moonshine and Monstrous Lie Superalgebras
Invent. Math. 109, 405-444 (1992). Richard E. Borcherds, Department of pure mathematics and mathematical statistics, 16 Mill Lane, Cambridge CB2 1SB, England. We prove Conway and Norton’s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by Frenkel, Lepowsky and Meurman. To do this we use the no-ghost theorem from string theory to construc...
متن کاملIwahori - Hecke type algebras associated with the Lie superalgebras A ( m , n ) , B ( m , n ) , C ( n ) and D ( m , n ) Hiroyuki Yamane
In this paper we give Iwahori-Hecke type algebras Hq(g) associated with the Lie superalgebras g = A(m,n), B(m,n), C(n) and D(m,n). We classify the irreducible representations of Hq(g) for generic q. Introduction Recently, motivated by a question posed by V. Serganova [S] and study of the Weyl groupoids [H1][H2] associated with Nichols algebras [AS1][AS2] including generalizations of quantum gro...
متن کاملGraded Lie Superalgebras, Supertrace Formula, and Orbit Lie Superalgebras
Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...
متن کامل