Regularity of vertex operator superalgebras

We prove that the regularity of a vertex operator superalgebra can be reduced to the semisimplicity of the category of its weak modules.Moreover,the rationality can be replaced by requiring that each 1/2Z+-graded module is a direct sum of irreducible weak modules.     

套代数弱闭模中的几何秩

由于几何秩在线性等距映射下是不变的,因此几何秩是研究算子代数线性等距映射的一个强有力的工具.证明了在一定条件下,套代数弱闭模中的n秩算子的几何秩的上、下界分别为n2和n(n+1)2,这表明套代数弱闭模中有限秩算子的充要条件是算子的几何秩有限.     

Stable rigged configurations for quantum affine algebras of nonexceptional types

For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type A can be expressed as a sum of that of type A with Littlewood–Richardson coefficients. Combining this result with Kirillov et al. (2002) [13] and Lecouvey et al. (2011) [18] we settle the X=M conjecture under the large rank hypothesis.     

Indépendance algébrique sur les T-modules

We study the transcendence degree (of the values at algebraic points) of the coordinate functions of a given one parameter subgroup on a simple g dimensional T-module. In such a situation, we obtain a lower bound for this transcendence degree depending on g and on the growth order of the parameter subgroup. As a particular case, one gets the finite characteristic analogue of a result of Siegel on the algebraic independence for the values of the classical Bessel function. Résumé. Nous obtenons une minoration du degré de transcendance d'un ensemble de valeurs en des points algébriques des fonctions coordonnées d'un sous-groupe à un paramètre d'un T-module simple, en fonction de l'ordre de croissance de ces dernières et de la dimension du T-module. Un cas particulier de ce résultat permet d'obtenir en caractéristique finie un analogue d'un résultat de Siegel sur l'indépendance algébrique des valeurs de la fonction de Bessel usuelle.     

相关扭曲Hopf模的基本同构定理与相关Yetter-Drinfel'd模

扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.     

On certain spaces of lattice diagram determinants

The aim of this work is to study some lattice diagram determinants Δ_L(X,Y) as defined in (Adv. Math. 142 (1999) 244) and to extend results of Aval et al. (J. Combin. Theory Ser. A, to appear). We recall that M_L denotes the space of all partial derivatives of Δ_L. In this paper, we want to study the space M_i,j^k(X,Y) which is defined as the sum of M_L spaces where the lattice diagrams L are obtained by removing k cells from a given partition, these cells being in the “shadow” of a given cell (i,j) in a fixed Ferrers diagram. We obtain an upper bound for the dimension of the resulting space M_i,j^k(X,Y), that we conjecture to be optimal. This dimension is a multiple of n! and thus we obtain a generalization of the n! conjecture. Moreover, these upper bounds associated to nice properties of some special symmetric differential operators (the “shift” operators) allow us to construct explicit bases in the case of one set of variables, i.e. for the subspace M_i,j^k(X) consisting of elements of 0 Y-degree.     

关于随机共轭空间的各种定义及随机线性泛函各种有界性的某些评论

中心目的是详细廉政论在随机共轭空间理论形成过程中所经历的三个阶段的工作，尤其指出了这三个阶段工作之间的联系及本质差别；给出了强有界、拓扑有界及几乎处处有界随机线性泛函之间的关系；亦指出了在概率赋范空间上线性算子理论研究中目前存在的不足．     

A Sato–Tate Law for Drinfeld Modules

We formulate and prove a Sato–Tate equidistribution law for Drinfeld modules.     

Gerbes,Clifford Modules and the Index Theorem

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.     

Descent Monomials, P-Partitions and Dense Garsia-Haiman Modules

A two-variable analogue of the descents monomials is defined and is shown to form a basis for the dense Garsia-Haiman modules. A two-variable generalization of a decomposition of a P-partition is shown to give the algorithm for the expansion into this descent basis. Some examples of dense Garsia-Haiman modules include the coinvariant rings associated with certain complex reflection groups.