相关论文: Annihilator varieties of distinguished modules of …

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restriction of Weyl modules from the algebraic group to the group of…

Let $G$ be connected reductive algebraic group defined over an algebraically closed field of characteristic $p > 0$ and suppose that $p$ is a good prime for the root system of $G$, the derived subgroup of $G$ is simply connected and the Lie…

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…

It is well known that the normaized characters of integrable highest weight modules of given level over an affine Lie algebra $\hat{\frak{g}}$ span an $SL_2(\mathbf{Z})$-invariant space. This result extends to admissible…

Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak k\subset\mathfrak g$ be a reductive in $\mathfrak g$ subalgebra. A $(\mathfrak g, \mathfrak k)$-module is a $\mathfrak g$-module which after restriction to $\mathfrak k$ becomes a…

In this manuscript we consider the extent to which an irreducible representation for a reductive Lie group can be realized as the sheaf cohomolgy of an equivariant holomorphic line bundle defined on an open invariant submanifold of a…

In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and…

Let $\frak g$ be a semisimple Lie algebra and $\frak k\subset\frak g$ be a reductive subalgebra. We say that a $\frak g$-module $M$ is a bounded $(\frak g, \frak k)$-module if $M$ is a direct sum of simple finite-dimensional $\frak…

Let $G$ be a connected, reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$ and $\mathfrak{g}=Lie(G)$. In this paper, we study representations of $\mathfrak{g}$ with a $p$-character $\chi$ of…

Given an affine Kac-Moody Lie algebra $\tilde{\mathfrak{g}}[\sigma]$ of arbitrary type, we determine certain minimal sets of annihilating fields of standard $\tilde{\mathfrak{g}}[\sigma]$-modules. We then use these sets in order to obtain a…

We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual…

Let $G$ be a real reductive Lie group and ${\tau}:G \longrightarrow GL(V)$ be a real reductive representation of $G$ with (restricted) moment map $m_{\ggo}: V-{0} \longrightarrow \ggo$. In this work, we introduce the notion of "nice space"…

We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

Let ${\mathfrak g}$ denote the complexified Lie algebra of $G={\mathrm O}(p,q)$ and $K$ a maximal compact subgroup of $G$. In the previous paper, we constructed $({\mathfrak g},K)$-modules associated to the finite-dimensional representation…

We construct a local deformation problem for residual Galois representations $\bar{\rho}$ valued in an arbitrary reductive group $\hat{G}$ which we use to develop a variant of the Taylor-Wiles method. Our generalization allows Taylor-Wiles…

Let $R$ be a commutative Noetherian ring, $\mathfrak a$ a proper ideal of $R$ and $N$ a non-zero finitely generated $R$-module with $N\neq \mathfrak a N$. Let $d$ (respectively $c$) be the smallest (respectively greatest) non-negative…

Let G be a reductive group over a non-archimedean local field and let S(G) be its Schwartz algebra. We compare Ext-groups of tempered G-representations in several module categories: smooth G-representations, algebraic S(G)-modules,…

Let \frak a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that {\rm Ann}_R(H_{\frak a}^{{\dim M}({\frak a}, M)}(M))= {\rm Ann}_R(M/T_R({\frak a}, M)), where T_R({\frak a}, M) is the largest…