منابع مشابه
The Pbw Filtration
In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebra b g. The n-th space of this filtration is spanned with the vectors x1. .. xsv, where xi ∈ b g, s ≤ n and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations....
متن کاملThe Pbw Filtration
In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras ĝ. The n-th space of this filtration is spanned by the vectors x1 . . . xsv, where xi ∈ ĝ, s ≤ n, and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. F...
متن کاملThe PBW Filtration, Demazure Modules and Toroidal Current Algebras⋆
Let L be the basic (level one vacuum) representation of the affine Kac–Moody Lie algebra ĝ. The m-th space Fm of the PBW filtration on L is a linear span of vectors of the form x1 · · ·xlv0, where l ≤ m, xi ∈ ĝ and v0 is a highest weight vector of L. In this paper we give two descriptions of the associated graded space L with respect to the PBW filtration. The “top-down” description deals with ...
متن کاملHomological Computations in PBW Modules
In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Exti (M,N) is provided when N is a centralizing bimodule. Mathematics Subject Classifications (2000): 16Z05, 16E30.
متن کامل0 an Explicit Formula for Pbw Quantization
0. Introduction We consider (possibly infinite dimensional) Lie algebras over a fixed field k of characteristic zero. Let g be a Lie algebra, S = Sg and U = Ug the symmetric and universal enveloping algebras, and F ⊂ F ⊂ · · · ⊂ U the coalgebra filtration F := k + g + g + · · ·+ g. Recall that the Poincaré-Birkhoff-Witt isomorphism between S and the associated graded ring GFU is induced by the ...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2009
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-09-00349-5