Related papers: Level-zero van der Kallen modules and specializati…

Motivated by the necessity to include so-called logarithmic operators in conformal field theories (Gurarie, 1993) at values of the central charge belonging to the logarithmic series c_{1,p}=1-6(p-1)^2/p, reducible but indecomposable…

Two-dimensional $\sigma$-models corresponding to coset CFTs of the type $ (\hat{\mathfrak{g}}_k\oplus \hat{\mathfrak{h}}_\ell )/ \hat{\mathfrak{h}}_{k+\ell}$ admit a zoom-in limit involving sending one of the levels, say $\ell$, to…

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

We establish the equality of the specialization $P_\lambda(x;q,0)$ of the Macdonald polynomial at $t=0$ with the graded character $X_\lambda(x;q)$ of a tensor product of "single-column" Kirillov-Reshetikhin (KR) modules for untwisted affine…

In this paper we clarify some asymptotic formulas given by Jaulent-Maire, which relate orders of finite quotients of S-infinitesimal T-classes l-groups $Cl^S_T(K_n)$ associated to finite layers $K_n$ of a Zl-extension $K_\infty/K$ over a…

We study the characters of simple modules in the parabolic BGG category of the affine Lie algebra in Deligne's category. More specifically, we take the limit of Weyl-Kac formula to compute the character of the irreducible quotient $L(X,k)$…

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…

We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…

The affine evaluation map is a surjective homomorphism from the quantum toroidal ${\mathfrak {gl}}_n$ algebra ${\mathcal E}'_n(q_1,q_2,q_3)$ to the quantum affine algebra $U'_q\widehat{\mathfrak {gl}}_n$ at level $\kappa$ completed with…

We introduce a new set of $q$-difference operators acting as raising operators on a family of symmetric polynomials which are characters of graded tensor products of current algebra ${\mathfrak g}[u]$ KR-modules \cite{FL} for ${\mathfrak…

Let $\Gamma \subset \mathbf{PU}(2,1)$ be a lattice which is not co-compact, of finite Bergman-covolume and acting freely on the open unit ball $\mathbf{B} \subset \mathbb{C}^2$. Then the compactification $X = \bar{\Gamma \setminus…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

We prove a localization theorem for affine $W$-algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight $\lambda$, we identify $\lambda$-monodromic Whittaker $D$-modules on…

Poincare Polynomial of a Kac-Moody Lie algebra can be obtained by classifying the Weyl orbit $W(\rho)$ of its Weyl vector $\rho$. A remarkable fact for Affine Lie algebras is that the number of elements of $W(\rho)$ is finite at each and…

Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…

Consider the general linear group $G=GL_{n}(K)$ defined over an infinite field $K$ of positive characteristic $p$. We denote by $\Delta(\lambda)$ the Weyl module of $G$ which corresponds to a partition $\lambda$. Let $\lambda, \mu $ be…

The category of weight modules $L_k(\mathfrak{sl}_2)\text{-wtmod}$ of the simple affine vertex algebra of $\mathfrak{sl}_2$ at an admissible level $k$ is neither finite nor semisimple and modules are usually not lower-bounded and have…

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type $(1,1)$ estimate of noncommutative maximal Calder\'{o}n-Zygmund operators, corresponding…

We consider arc spaces for the compositions of Pluecker and Veronese embeddings of the flag varieties for simple Lie groups of types ADE. The arc spaces are not reduced and we consider the homogeneous coordinate rings of the corresponding…