相关论文: Lie algebra modules which are locally finite over …

We study cohomological induction for a pair $(\frak g,\frak k)$, $\frak g$ being an infinite dimensional locally reductive Lie algebra and $\frak k \subset\frak g$ being of the form $\frak k_0 + C_\gg(\frak k_0)$, where $\frak…

For any reductive Lie algebra $\mathfrak{g}$ and commutative, associative, unital algebra $S$, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S $ with finite weight multiplicities. In particular, any…

Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…

Let $\frak g$ be a reductive Lie algebra over $\bold C$. We say that a $\frak g$-module $M$ is a generalized Harish-Chandra module if, for some subalgebra $\frak k \subset\frak g$, $M$ is locally $\frak k$-finite and has finite $\frak…

In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra $\widehat{\mathcal{L}}=\mathcal{W}\ltimes(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm…

This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of…

In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g}…

Let $A=\mathbb{C}[t_1^{\pm1},t_2^{\pm1}]$ be the algebra of Laurent polynomials in two variables and $B$ be the set of skew derivations of $A$. Let $L$ be the universal central extension of the derived Lie subalgebra of the Lie algebra…

We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…

We prove a general existence result for infinite-dimensional admissible (g;k)-modules, where g is a reductive finite-dimensional complex Lie algebra and k is a reductive in g algebraic subalgebra.

For any complex reductive Lie algebra g and any locally finite g-module V, we extend to the tensor product of U(g) with V the Harish-Chandra description of g-invariants in the universal enveloping algebra U(g).

We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are defined via a geometric realization in terms…

We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras $(\g,\k)$,…

It is shown that the support of an irreducible weight module over the Schr\"{o}dinger-Virasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…

We use analogues of Enright's and Arkhipov's functors to determine the quiver and relations for a category of $\mathfrak{sl}_2 \ltimes L(4)$-modules which are locally finite (and with finite multiplicities) over $\mathfrak{sl}_2$. We also…

We continue the study of the fundamental series of generalized Harish-Chandra modules initiated in [PZ2]. Generalized Harish-Chandra modules are (g,k)-modules of finite type where g is a semisimple Lie algebra and k \subset g is a reductive…

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 $\frak g$ be a reductive Lie algebra over an algebraically closed field of characteristic $p>0$. In this paper, we study the representations of $\frak g$ with a $p$-character $\chi$ of standard Levi form associated with a given subset…

Let $G$ be a connected reductive linear algebraic group over a field $k$. Using ideas from geometric invariant theory, we study the notion of $G$-complete reducibility over $k$ for a Lie subalgebra $\mathfrak h$ of the Lie algebra…

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie…