Related papers: The PBW filtration
Let $L$ be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra $\hat{\mathfrak g}$. The $m$-th space $F_m$ of the PBW filtration on $L$ is a linear span of vectors of the form $x_1... x_lv_0$, where $l\le m$,…
We study the PBW filtration on the highest weight representations $V(\la)$ of $\msl_{n+1}$. This filtration is induced by the standard degree filtration on $U(\n^-)$. We give a description of the associated graded $S(\n^-)$-module $gr…
We study the PBW-filtration on the highest weight representations $V(\la)$ of the Lie algebras of type ${\tt A}_{n}$ and ${\tt C}_{n}$. This filtration is induced by the standard degree filtration on $\U(\fn^-)$. In previous papers, the…
We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type $\tt B_n$. We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional…
We study the PBW filtration on the highest weight representations $V(\la)$ of $\msp_{2n}$. This filtration is induced by the standard degree filtration on $U(\n^-)$. We give a description of the associated graded $S(\n^-)$-module $gr…
We study the PBW filtration on the irreducible highest weight representations of simple complex finite-dimensional Lie algebras. This filtration is induced by the standard degree filtration on the universal enveloping algebra. For certain…
We will introduce an $\mathbb{N}$-filtration on the negative part of a quantum group of type $A_n$, such that the associated graded algebra is a q-commutative polynomial algebra. This filtration is given in terms of the representation…
We study the Brylinski filtration induced by a principal Heisenberg subalgebra of an affine Kac-Moody algebra $\mathfrak{g}$, a notion first introduced by Slofstra. The associated graded space of this filtration on dominant weight spaces of…
We develop an elementary method for proving the PBW theorem for associative algebras with an ascending filtration. The idea is roughly the following. At first, we deduce a proof of the PBW property for the {\it ascending} filtration (with…
To every $h + \mathbb{N}$-graded module $M$ over an $\mathbb{N}$-graded conformal vertex algebra $V$, we associate an increasing filtration $(G^pM)_{p \in \mathbb{Z}}$ which is compatible with the filtrations introduced by Haisheng Li. The…
We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r=2 and r=3. This combinatorial object appears as a label of a basis of certain subspace $W(\Lambda)$ of level-$k$ integrable highest…
We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…
This paper classifies irreducible, integrable highest weight modules for "current Kac-Moody Algebras" with finite dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many…
In this paper we study the family of prime irreducible representations of quantum affine $\lie{sl}_{n+1}$ which arise from the work of D. Hernandez and B. Leclerc. These representations can also be described as follows: the highest weight…
We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an…
In the first part of the paper we give the denominator identity for all simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate invariant bilinear form. We give also a character and (super) dimension formulas for all…
In this paper, we study the representation theory for the affine Lie algebra $\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the irreducible highest weight modules of $\H$. Furthermore, we give a necessary and sufficient…
We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody…
This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of the W-algebra $W_k(g)$ associated with a…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.