The Restricted Kirillov–Reshetikhin Modules for the Current and Twisted Current Algebras

We define a family of graded restricted modules for the polynomial current algebra associated to a simple Lie algebra. We study the graded character of these modules and show that they are the same as the graded characters of certain Demazure modules. In particular, we see that the specialized characters are the same as those of the Kirillov Reshetikhin modules for quantum affine algebras.VC was partially supported by the NSF grant DMS-0500751.     

Demazure Modules and Perfect Crystals

We give a criterion for the Demazure crystal defined by Kashiwara to have a tensor product structure. We study the symmetric tensor case, and see some Demazure characters are expressed using Kostka-Foulkes polynomials. Received: 29 August 1996 / Accepted: 18 July 1997     

Boundary Structure and Module Decomposition of the Bosonic Z2 Orbifold Models with R=1/2k

The Z₂ bosonic orbifold models with compactification radius R²=1/2k are examined in the presence of boundaries. Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, one arrives at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, compatible with the modular transformations of the characters. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.     

New Weyl groups forA 1 (1) and characters of singular highest weight modules

We consider singular Verma modules overA ₁ ⁽¹⁾ , i.e., Verma modules for which the central charge is equal to minus the dual Coxeter number. We calculate the characters of certain factor modules of these Verma modules. In one class of cases we are able to prove that these factor modules are actually the irreducible highest modules for those highest weights. We introduce new Weyl groups which are infinitely generated abelian groups and are proper subgroups or isomorphic between themselves. Using these Weyl groups we can rewrite the character formulae obtained in the paper in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semisimple Lie algebras (respectively Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras) so that the new Weyl groups play the role of the usual Weyl group (respectively affine Weyl group).     

Affine Vertex Operator Algebras and Modular Linear Differential Equations

In this paper, we list all affine vertex operator algebras of positive integral levels whose dimensions of spaces of characters are at most 5 and show that a basis of the space of characters of each affine vertex operator algebra in the list gives a fundamental system of solutions of a modular linear differential equation. Further, we determine the dimensions of the spaces of characters of affine vertex operator algebras whose numbers of inequivalent simple modules are not exceeding 20.     

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. Furthermore, we prove that certain parabolic BGG categories over the general linear algebra and over the general linear superalgebra are equivalent. We also verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category of the general linear superalgebra.     

Generating functions for characters and weight multiplicities of irreducible (4)-modules

Generating functions for the characters of the irreducible representations of simple Lie algebras are rational functions where both the numerator and denominator can be expressed as polynomials in the characters corresponding to the fundamental weights. They encode much information on the representation theory of the algebra, but their explicit expressions are in general very complicated. In fact, it seems that rank three is the highest rank tractable. In this paper, we use a method based on the quantum Calogero-Sutherland model to compute the full generating function for the characters of irreducible modules over the complex Lie algebra (4), and exploit this result to obtain also generating functions giving the multiplicities of some low order weights in all representations. We have applied the same method to compute the generating function for the characters of the modules the other rank three simple Lie algebras, but in these cases the full expressions are very long and appear only in the arXiv version of the paper (arXiv:1705.03711 [math-ph]). Nevertheless, when the generating functions are limited to some particular subsets of characters, the results are quite simple and we present them here.     

Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra \({\mathfrak{q}(n)}\). It is given in terms of the Brundan’s work on finite-dimensional integer weight \({\mathfrak{q}(n)}\)-modules by means of Lusztig’s canonical basis. Using this viewpoint we compute the characters of the finite-dimensional half-integer weight irreducible modules. For a large class of irreducible modules whose highest weights are of special types (i.e., totally connected or totally disconnected) we derive closed-form character formulas that are reminiscent of the Kac–Wakimoto character formula for basic Lie superalgebras.     

A Weyl group for the Virasoro andN=1 super-Virasoro algebras

We introduce a Weyl group for the highest weight modules over the Virasoro algebra and the Neveu-Schwarz and Ramond superalgebras. Using this group we rewrite the character formulae for the irreducible highest weight modules over these algebras in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semi-simple Lie algebras (and also of the Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras). This is the same group we introduced recently in order to rewrite in a similar manner the characters of the singular highest weight modules over the affine Kac-Moody algebraA ₁ ⁽¹⁾ .     

边界扫描测试在数字电路自动测试系统中的研究与应用[BT)]

边界扫描测试是当前数字电路模块故障隔离的主要手段,但测试能力受到模块可测试性设计限制,其它方面作用也被忽略。文中对数字电路自动测试系统设计提出了边界扫描测试应用技术,包括系统自检测试,模块功能测试和模块故障隔离。在系统自检测试中应用边界扫描,提高了设备自检故障隔离精度;而对于模块功能测试,边界扫描测试技术提供了一种新的选择;在故障隔离中扩展和延伸应用边界扫描技术,突破了模块自身测试性的限制,提高了边界扫描测试的故障覆盖率和故障隔离精度。通过实际测试验证表明,该设计方法稳定可靠,同时提升了测试系统自身和模块的测试能力和隔离精度。     

An admissible level $$\widehat{\mathfrak {osp}} \left( 1 \big \vert 2 \right) $$-model: modular transformations and the Verlinde formula

The modular properties of the simple vertex operator superalgebra associated with the affine Kac–Moody superalgebra \(\widehat{{\mathfrak {osp}}} (1|2)\) at level \(-\frac{5}{4}\) are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed.     

Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu’s theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover ${SL_2(\mathbb{Z})}$ S L 2 ( Z ) -invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain ‘odd traces’ on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional ${SL_2(\mathbb{Z})}$ S L 2 ( Z ) -invariant space. We close the paper with several examples.     

金属切削变形与显微高速摄影分析

运用显微高速摄影技术分析了切削过程中金属显微组织塑性变形规律。结果指出,切削中金属晶粒变形具有不均匀性和多晶体变形协调性,以晶粒为单元发生了波浪式起伏立体型变化,但受到晶界的制约。     

Skew Young Diagram Method in Spectral Decomposition of Integrable Lattice Models

The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra is studied. We give a one-to-one correspondence between the spin configurations and the semistandard tableaux of skew Young diagrams. As a result we obtain a formula of the characters for the degeneracy of the spectrum in terms of skew Schur functions. We conjecture that our result describes the -module contents of the Yangian -module structures of the level 1 integrable modules of the affine Lie algebra . An analogous result is obtained also for a vertex model associated to the quantized twisted affine algebra , where characters appear for the degeneracy of the spectrum. The relations to the spectrum of the Haldane-Shastry and the Polychronakos models are also discussed. Received: 28 July 1996 / Accepted: 11 October 1996     

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

We present a simple bijection between restricted Bressoud lattice paths and paths in regime II of the Andrews–Baxter–Forrester restricted solid–on–solid model. Both types of paths describe states in parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.      

EPICS在加速器控制系统中的应用

 介绍了当前国内外大型加速器实验室采用的主流控制系统软件开发工具EPICS的总体结构和特点,主要介绍了ASYN结构和特点,以及对使用ASYN软件包建立磁铁电源串口设备支持模块进行的研究,并将其应用于中国工程物理研究院驱动自由电子激光的30 MeV直线加速器磁铁电源控制系统中。同时还具体介绍了磁铁电源控制系统的结构以及系统软件设计,为直线加速器控制系统的建设做好准备工作。使用EPICS开发工具建立的加速器控制系统可以满足实验要求的高可靠性和高稳定性,从而为自由电子激光实验提供高品质束流。     

On q-Deformed $${{\mathfrak{gl}}_{\ell+1}}$$-Whittaker Function III

In this paper, we identify q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions with a specialization of the Macdonald polynomials. This provides a representation of q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions in terms of the Demazure characters of affine Lie algebra [^(\mathfrakgl)]_l+1{\widehat{\mathfrak{gl}}_{\ell+1}}. We also define a system of dual Hamiltonians for q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Toda chains and give a new integral representation for the q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions. Finally, we represent the q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker function as a matrix element of a quantum torus algebra.     

K-matrices for 2D conformal field theories

In this paper we examine fermionic type characters (Universal Chiral Partition Functions) for general 2D conformal field theories with a bilinear form given by a matrix of the form . We provide various techniques for determining these K-matrices, and apply these to a variety of examples including (higher level) WZW and coset conformal field theories. Applications of our results to fractional quantum Hall systems and (level restricted) Kostka polynomials are discussed.     

Lie Superalgebras and Irreducibility of $$A_1^{(1)}$$ –Modules at the Critical Level

We introduce the infinite-dimensional Lie superalgebra and construct a family of mappings from a certain category of –modules to the category of –modules at the critical level. Using this approach, we prove the irreducibility of a large family of –modules at the critical level parameterized by . As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations. Partially supported by the MZOS grant 0037125 of the Republic of Croatia     

Fredholm modules for quantum Euclidean spheres

The quantum Euclidean spheres, S_q^N−1, are (noncommutative) homogeneous spaces of quantum orthogonal groups, SO_q(N). The *-algebra A(S^N−1_q) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres S_q^N−1. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i.e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra A(S^N−1_q).