Odd Singular Vector Formula for General Linear Lie Superalgebras
نویسندگان
چکیده
منابع مشابه
Graded 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 کاملHowe Duality and Combinatorial Character Formula for Orthosymplectic Lie Superalgebras
We study the Howe dualities involving the reductive dual pairs (O(d), spo(2m|2n)) and (Sp(d), osp(2m|2n)) on the (super)symmetric tensor of C ⊗ C. We obtain complete decompositions of this space with respect to their respective joint actions. We also use these dualities to derive a character formula for these irreducible representations of spo(2m|2n) and osp(2m|2n) that appear in these decompos...
متن کاملCrystal graphs for general linear Lie superalgebras and quasi-symmetric functions
We give a new representation theoretic interpretation of the ring of quasisymmetric functions. This is obtained by showing that the super analogue of the Gessel’s fundamental quasi-symmetric function can be realized as the character of an irreducible crystal for the Lie superalgebra gln|n associated to its non-standard Borel subalgebra with a maximal number of odd isotropic simple roots. We als...
متن کاملCOMPOSITION FACTORS OF KAC-MODULES FOR THE GENERAL LINEAR LIE SUPERALGEBRAS glm|n
The composition factors of Kac-modules for the general linear Lie superalgebras gl m|n are explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.
متن کاملHom-Lie Superalgebras and Hom-Lie admissible Superalgebras
The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one paramete...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
سال: 2019
ISSN: 2304-7895,2304-7909
DOI: 10.21915/bimas.2019401