相关论文: A classification of irreducible Wakimoto modules f…
We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra $\widehat{sl_2}$ of type $A_1^{(1)}$ with noncritical level which are also irreducible Whittaker modules over $\widetilde{sl_2}…
We investigate the irreducible smooth $\widehat{\mathfrak{sl}}_{2}$-modules recently constructed in [Adv. Math. 481 (2025), 110559, 34 pages, arXiv:2404.03855], and demonstrate that these modules admit a Wakimoto-type realization at both…
We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the…
Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…
We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…
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 study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such…
We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal…
We construct a class of modules for extended affine Lie algebra $\widetilde{\frak{gl}_l({\bc_q})}$ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.
The irreducible representations of the Witt algebra $W$ are completely known. A classification of the irreducible $U_\chi(W)$--modules was first established by Chang and later simplified by Strade. The aim of this article is to give a…
The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…
In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebra $\hat{\g}$ by exploiting basic formal variable techniques. We define and study two categories ${\mathcal{E}}$ and…
We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules…
In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…
In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…
In this paper, we used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. The structures of the representations over the general linear…
It is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series.…
We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex…
In this paper, we study a class of $\Z_d$-graded modules, which are constructed using Larsson's functor from $\sl_d$-modules $V$, for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the…