相关论文: Non-Minimality of Certain Irregular Coherent Premi…

We obtain character formulas of minimal affinizations of representations of quantum groups when the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin…

We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type E6. For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit…

We study the graded limits of minimal affinizations over a quantum loop algebra of type D in the regular case. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and also give their defining…

We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin…

We define the categories of weight-finite modules over the type $\mathfrak a_1$ quantum affine algebra $\dot{\mathrm{U}}_q(\mathfrak a_1)$ and over the type $\mathfrak a_1$ double quantum affine algebra $\ddot{\mathrm{U}}_q(\mathfrak a_1)$…

We find modular transformations of normalized characters for the following $W$-algebras: (a) $W^{min}_k(\frak{g})$, where $\frak{g}=D_n \, (n \geq 4)$, or $E_6$, $E_7$, $E_8$, and $k$ is a negative integer $\geq -2$, or $\geq…

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a…

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…

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of the same rank as $G$. In the recent paper of Huang, Pand\v{z}i\'{c} and Vogan, it was shown that the admissible $\Theta$--stable parabolic subalgebras…

The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type $G_2$. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and obtain defining…

We construct quasi-particle bases of principal subspaces of standard modules $L(\Lambda)$, where $\Lambda=k_0\Lambda_0+k_j\Lambda_j$, and $\Lambda_j$ denotes the fundamental weight of affine Lie algebras of type $B_l^{(1)}$, $C_l^{(1)}$,…

A connected undirected graph $G = (V,E)$ is lower conformally rigid if uniform edge weights maximize the second smallest Laplacian eigenvalue $\lambda_2(w)$ over all normalized edge weights $w$, and upper conformally rigid if uniform edge…

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 $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

We continue our study of minimal affinizations for algebras of type D, E.

We describe a categorification of the Double Affine Hecke Algebra (${\mathcal{H}\kern -.4em\mathcal{H}}$) associated with an affine Lie algebra $\widehat{\mathfrak{g}}$, including a categorification of the polynomial representation and…

In this paper, we show that the Dirac cohomology $H_{D}(L(\lambda))$ of a simple highest weight module $L(\lambda)$ in $\mathcal{O}^\mathfrak{p}$ can be parameterized by a specific set of weights: a subset $\mathcal{W}_I(\lambda)$ of the…

In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type…