相关论文: On the annihilator variety of a highest weight mod…

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

We present an algorithm which computes the annihilator in ${\rm U}(\frak{sl}(\infty))$ of any simple highest weight $\frak{sl}(\infty)$-module $L_\frak b(\lambda)$. This algorithm is based on an infinite version of the Robinson-Schensted…

Let $\mathfrak{g}$ be a complex Kac-Moody algebra, with Cartan subalgebra $\mathfrak{h}$. Also fix a weight $\lambda\in\mathfrak{h}^*$. For $M(\lambda)\twoheadrightarrow V$ an arbitrary highest weight $\mathfrak{g}$-module, we provide a…

Let $\mathfrak{g}$ be a complex simple Lie algebra. A simple $\mathfrak{g}$-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of…

Let g be a semisimple Lie algebra with h a Cartan subalgebra. The orbit method attempts to assign representations of g to orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits which should lead to highest…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

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…

We completely determine the minimal polynomial of an arbitrary simple highest weight module $L(\lambda)$ over a complex classical Lie algebra $\mathfrak{g}\subseteq\mathfrak{gl}_N$ relative to its defining module $\pi=\mathbb{C}^{N}$. These…

In this paper, we present a uniform formula of Lusztig's $ \mathbf{a}$-functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions of simple highest weight modules of classical Lie algebras,…

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…

Fix any complex Kac-Moody Lie algebra $\mathfrak{g}$, and Cartan subalgebra $\mathfrak{h}\subset \mathfrak{g}$. We study arbitrary highest weight $\mathfrak{g}$-modules $V$ (with any highest weight $\lambda\in \mathfrak{h}^*$, and let…

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…

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…

We study a category of modules over $\mathfrak{gl}(\infty)$ analogous to category $\mathcal O$. We fix adequate Cartan, Borel and Levi-type subalgebras $\mathfrak h, \mathfrak b$ and $\mathfrak l$ with $\mathfrak l \cong…

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…

We provide a micro-local necessary condition for distinction of admissible representations of real reductive groups in the context of spherical pairs. Let $\bf G$ be a complex algebraic reductive group, and $\bf H\subset G$ be a spherical…

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…

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…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask…