相关论文: On the Category of Harish-Chandra Block Modules
This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…
In this paper, we give a new approach to classify all simple Harish-Chandra modules for the N=1 Ramond algebra based on the so called A-cover theory developed in \cite{BF}
In this paper, using the theory of $\A$-cover developed in \cite{B1,BF1}, we completely classify all simple Harish-Chandra modules over the high rank $W$-algebra $W(2,2)$. As a byproduct, we obtain the classification of simple…
We consider the category of Harish-Chandra modules for ${\rm SL}_2(\mathbb R)$ as a module over the category of finite-dimensional representations of ${\rm SL}(2)$ with respect to the tensor product. In this note we use classical results…
We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal bounded module over a cuspidal map superalgebra. Further on,…
Let $G$ be an arbitrary additive subgroup of $C$ and $Vir[G]$ the corresponding generalized Virasoro algebra. In the present paper, irreducible weight modules with finite dimensional weight spaces over $Vir[G]$ are completely determined.…
The notion of a Harish-Chandra bimodule, i.e. finitely generated $U(\mathfrak{g})$-bimodule with locally finite adjoint action, was generalized to any filtered algebra in a work of Losev [Ivan Losev, Dimensions of irreducible modules over…
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho)[s]$ for $s=0,\frac12$.…
We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional.…
We prove that any irreducible Harish-Chandra modules for a class of Lie algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series.These algebras are…
We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maa{\ss} forms with exponential growth allowed at the cusps. This extends work by Schulze-Pillot and parallels recent work by…
In this paper, it is proved that all irreducible Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro algebra are of intermediate series (all weight spaces are 1-dimensional).
The distribution of the unipotent modules (in non-defining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph…
It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains…
Let $\mathcal{A}_n = \C[t_1^{\pm1}, t_2^{\pm1}, \ldots, t_n^{\pm1}]$, and let $\EuScript{D}_n$ denote the divergence-zero subalgebra of $\text{Der}\,(\mathcal{A}_n)$. In this paper, we classify irreducible Harish-Chandra modules over the…
A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is…
With the $\Omega$-operators for the Virasoro algebra \cite{BF} and the super Virasoro algebra in \cite{CL, CLL}, we get the $\Omega$-operators for the Ovsienko-Roger superalgebras in this paper and then use it to classify all simple…
We study Harish-Chandra representations of Yangian for gl(2). We prove an analogue of Kostant theorem showing that resterited Yangians for gl(2) are free modules over certain maximal commutative subalgebras. We also study the categories of…
Koenig and Xi introduced {\em affine cellular algebras}. Kleshchev and Loubert showed that an important class of {\em infinite dimensional} algebras, the KLR algebras $R(\Gamma)$ of finite Lie type $\Gamma$, are (graded) affine cellular; in…
We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We…