Related papers: Classification of simple Harish-Chandra modules ov…
We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give…
For any irreducible Harish-Chandra module $V$ over the gap-$p$ Virasoro algebra, we determine the condition for $V$ to be unitary.
The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…
For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that…
We prove a category equivalence between algebraic supergroups and Harish-Chandra pairs over a commutative ring which is $2$-torsion free. The result is applied to re-construct the Chevalley $\mathbb{Z}$-supergroups constructed by Fioresi…
This paper studies restricted modules of gap-$p$ Virasoro algebra $\L$ and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted $\L$-modules of level…
In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded…
In this paper, we first obtain a general result on sufficient conditions for tensor product modules to be simple over an arbitrary Lie algebra. We classify simple modules with a nice property over the infinite-dimensional Heisenberg algebra…
We classify the simple modules for the rational Cherednik algebra that are irreducible when restricted to W, in the case when W is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in…
According to V. Kac and J. van de Leur, the superconformal algebras are the simple $\Z$-graded Lie superalgebras of growth one which contains the Witt algebra. We describe an explicit classification of all cuspidal modules over the known…
In this paper, Whittaker modules for the W-algebra W(2,2) are studied. We obtain analogues to several results from the classical setting and the case of the Virasoro algebra, including a classification of simple Whittaker modules by central…
In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a…
Intrigued by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra, we give an analogous result for a class of Block type Lie algebras $\BB$, where the parameter $q$ is a nonzero complex number. We also…
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
We determine all premodular subcategories and modular tensor subcategories in the module categories of Virasoro vertex operator algebras $L(c_{p,q},0)$ and the module categories of the simple current extensions of $L(c_{p,p+1},0)$.
For coprime $p,q\in\mathbb{Z}_{\geq 2}$, the triplet vertex operator algebra $W_{p,q}$ is a non-simple extension of the universal Virasoro vertex operator algebra of central charge $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and it is a basic example…
We study Harish-Chandra bimodules for the rational Cherednik algebra associated to the symmetric group $S_{n}$. In particular, we show that for any parameter $c \in \mathbb{C}$, the category of Harish-Chandra $H_{c}$-bimodules admits a…
Inspired by recent activities on Whittaker modules over various (Lie) algebras we describe some general framework for the study of Lie algebra modules locally finite over a subalgebra. As a special case we obtain a very general setup for…
We find a canonical $N{=}2$ superconformal algebra (SCA) in the BRST complex associated to any affine Lie algebra $\hat{\mathbf{h}}$ with $\mathbf{h}$ semisimple. In contrast with the similar known results for the Virasoro, $N{=}1$…
We classify all simple $W_n$-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes…