相关论文: Gelfand-Kirillov dimensions and associated varieti…

In this paper, we give an efficient algorithm to compute the Gelfand-Kirillov dimensions of simple highest weight modules of exceptional Lie algebras. By using the Sommers-Achar duality, we also determine the annihilator varieties of these…

We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand--Kirillov dimension of highest weight Harish-Chandra module…

We give the first positive formulas for the weights of every simple highest weight module $L(\lambda)$ over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight, we also express the weights of $L(\lambda)$ as an…

Let $ (G,K) $ be an irreducible Hermitian symmetric pair of non-compact type with $G=SU(p,q)$, and let $ \lambda $ be an integral weight such that the simple highest weight module $ L(\lambda) $ is a Harish-Chandra $ (\mathfrak{g},K)…

Let $\mathfrak{g}$ be a classial Lie algebra and $\mathfrak{p}$ be a maximal parabolic subalgebra. Let $M$ be a generalized Verma module induced from a one dimensional representation of $\mathfrak{p}$. Such $M$ is called a scalar type…

Let $L(\lambda)$ be a highest weight Harish-Chandra module with highest weight $\lambda$. When the associated variety of $L(\lambda)$ is not maximal, that is, not equal to the nilradical of the corresponding parabolic subalgebra, we prove…

Let $\mathfrak{g}$ be a classical complex simple Lie algebra. Let $L(\lambda)$ be a highest weight module of $\mathfrak{g}$ with highest weight $\lambda-\rho$, where $\rho$ is half the sum of positive roots. The associated variety of the…

We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…

Let $G$ be a Hermitian type Lie group with the complexified Lie algebra $\mathfrak{g}$. We use $L(\lambda)$ to denote a highest weight Harish-Chandra $G$-module with infinitesimal character $\lambda$. Let $w$ be an element in the Weyl group…

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…

Let $G$ be a Hermitian type Lie group with maximal compact subgroup $K$. Let $L(\lambda)$ be a highest weight Harish-Chandra module of $G$ with the infinitesimal character $\lambda$. By using some combinatorial algorithm, we obtain a…

Let $\mathfrak{g}$ be a simple complex Lie algebra of classical type with a Cartan subalgebra $\mathfrak{h}$. We fix a standard parabolic subalgebra $\mathfrak{p}\supset \mathfrak{h}$. The socular simple modules are just those highest…

Let $G_{\mathbb{R}}$ be a Lie group of Hermitian type, and $L(\lambda)$ a highest weight Harish-Chandra module of $G_{\mathbb{R}}$ with highest weight $\lambda$. In this article, we exhibit a bijection between the set of connected Dynkin…

Let $\mathcal{O}_q(G)$ be the quantized algebra of regular functions on a semisimple simply connected compact Lie group $G$. Simple unitarizable left $\mathcal{O}_q(G)$-module are classified. In this article, we compute their…

In this paper we study realizations of highest weight modules for the complex Lie algebra $\mathfrak{gl}_n$ with respect to non-standard Gelfand-Tsetlin subalgebras. We also provide sufficient conditions for such subalgebras to have a…

In this short note we announce three formulas for the set of weights of various classes of highest weight modules $\V$ with highest weight \lambda, over a complex semisimple Lie algebra $\lie{g}$ with Cartan subalgebra $\lie{h}$. These…

The present paper continues the work of [10] and [6]. For any symmetrizable generalized Cartan Matrix $C$ and the corresponding quantum group $\mathbf{U}$, we consider the associated quiver $Q$ with an admissible automorphism $a$. We…

In this paper we study general highest weight modules $\mathbb{V}^\lambda$ over a complex finite-dimensional semisimple Lie algebra $\mathfrak{g}$. We present three formulas for the set of weights of a large family of modules…

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n, F)-modules that appeared in the Z^2-graded oscillator generalizations of the classical theorem on harmonic polynomials…

For the $n$-dimensional multiparameter quantum torus algebra $\Lambda_{\mathfrak q}$ over a field $k$ defined by a multiplicatively antisymmetric matrix $\mathfrak q = (q_{ij})$ we show that in the case when the torsion-free rank of the…