Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra
نویسندگان
چکیده
منابع مشابه
Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra
The Fock space of m+p bosonic and n+q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p|n+q. Its tensor powers decompose into direct sums of infinite dimensional irreducible highest weight glm+p|n+q-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irredu...
متن کاملCharacter and Dimension Formulae for Finite Dimensional Irreducible Representations of the General Linear Superalgebra
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...
متن کاملCharacter and Dimension Formulae for General Linear Superalgebra
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary r-fold atypical gl m|n-Kac-module and the set of composition factors of some r-fold atypical gl r|r-Kac-module. The result of...
متن کاملCOMPOSITION FACTORS OF KAC-MODULES FOR THE GENERAL LINEAR LIE SUPERALGEBRA glm|n
The composition factors of Kac-modules for the general linear Lie superalgebra gl m|n is explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.
متن کاملEquivalence of Blocks for the General Linear Lie Superalgebra
We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie superalgebra to an integral block of O for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of O.
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: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00538-6