Volume 4 (2004), Number 4. Abstracts

M. Jimbo, T. Miwa, and Y. Takeyama. Counting Minimal Form Factors of the Restricted sine-Gordon Model [PDF]

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a q-analog of the space of conformal coinvariants associated with Uq(\widehat{sl}_2) with q = \sqrt{−1}. We prove that its character is given by the restricted Kostka polynomial multiplied by a simple factor. As a result, we obtain a formula for the truncated character of the total space of local fields in terms of the Virasoro characters.

Keywords. Form factor, restricted sine-Gordon model.

2000 Mathematics Subject Classification. 81T40, 81R50.

M. Kashiwara. t-Structures on the Derived Categories of Holonomic D-Modules and Coherent O-Modules [PDF]

We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial t-structure on the derived category of constructible sheaves via Riemann—Hilbert correspondence. We give also the condition for a decreasing sequence of families of supports to give a t-structure on the derived category of coherent O-modules.

Keywords. D-modules, t-structures, Riemann—Hilbert correspondence.

2000 Mathematics Subject Classification. Primary: 32C38; Secondary: 18E30.

G. Lusztig. Parabolic Character Sheaves, II [PDF]

The theory of character sheaves on a reductive group is extended to a class of varieties which includes the strata of the De Concini—Procesi completion of an adjoint group.

Keywords. Reductive group, parabolic group, perverse sheaf, character sheaf.

2000 Mathematics Subject Classification. 20G99.

I. MirkoviŠ. Character Sheaves on Reductive Lie Algebras [PDF]

The paper develops a linearized notion of Lusztig's character sheaves (on Lie algebras rather then on groups), which contains Lusztig's class of character sheaves on Lie algebras. The theory is independent of the characteristic p of the field, and we use it to provide elementary proofs of some results of Lusztig (for instance, the observation that on groups all cuspidal sheaves are character sheaves).

Keywords. Character, sheaf, Lie algebra, Lusztig.

2000 Mathematics Subject Classification. 14.

R. Nest and B. Tsygan. Remarks on Modules over Deformation Quantization Algebras [PDF]

We study the Maslov theory of canonical operator and the H÷rmander theory of distributions given by oscillatory integrals from the point of view of deformation quantization.

Keywords. Lagrangian manifold, deformation quantization.

2000 Mathematics Subject Classification. 53D12, 53D55.

A. Odesskii. Bihamiltonian Elliptic Structures [PDF]

We construct three compatible quadratic Poisson structures such that generic linear combination of them is associated with elliptic Sklyanin algebra in n generators. Symplectic leaves of this elliptic Poisson structure is studied. Explicit formulas for Casimir elements are obtained.

Keywords. Bihamitonian structure, Lenard scheme, elliptic algebras, symplectic leaves, Casimir elements.

2000 Mathematics Subject Classification. 14, 79.

P. Sherman and A. Zelevinsky. Positivity and Canonical Bases in Rank 2 Cluster Algebras of Finite and Affine Types [PDF]

The main motivation for the study of cluster algebras initiated in [6], [3], [1] was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic groups. In this paper, we introduce and explicitly construct the canonical basis for a special family of cluster algebras of rank 2.

Keywords. Cluster algebras, affine root systems, Newton polygons.

2000 Mathematics Subject Classification. Primary: 16S99; Secondary: 05E15, 22E46.

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Moscow Mathematical Journal
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© 2004, Independent University of Moscow

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