Representations of Toroidal General Linear Superalgebra
نویسندگان
چکیده
منابع مشابه
Character 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 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 کاملIrreducible Characters of General Linear Superalgebra and Super Duality
We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...
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 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: Communications in Algebra
سال: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2012.660258