258 research outputs found
Compatibility of systems of linear ordinary differential equations with variable coefficients
Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups
We introduce and study action of quantum groups on skew polynomial rings and
related rings of quotients. This leads to a ``q-deformation'' of the
Gel'fand-Kirillov conjecture which we partially prove. We propose a
construction of automorphisms of certain non-commutaive rings of quotients
coming from complex powers of quantum group generators; this is applied to
explicit calculation of singular vectors in Verma modules over
U_{q}(\gtsl_{n+1}).
We finally give a definition of a connection with coefficients in a ring
of skew polynomials and study the structure of quantum group modules twisted by
a connection.Comment: 25 page
Analytic Expressions for Singular Vectors of the Superconformal Algebra
Using explicit expressions for a class of singular vectors of the
(untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and
Kent, we show that the analytically extended Verma modules contain two linearly
independent neutral singular vectors at the same grade. We construct this two
dimensional space and we identify the singular vectors of the original Verma
modules. We show that in some Verma modules these expressions lead to two
linearly independent singular vectors which are at the same grade and have the
same charge.Comment: 35 pages, LATE
Singular vectors by Fusions in affine su(2)
Explicit expressions for the singular vectors in the highest weight
representations of are obtained using the fusion formalism of
conformal field theory.Comment: 7 page
Modification of Structure and Strength Properties of Permanent Joints Under Laser Beam Welding with Application of Nanopowder Modifiers
In the paper we present the results of experimental study of specially prepared nanosize metal-ceramic compositions impact upon structure, microhardness and mechanical properties of permanent joints produced by laser-beam welding of steel and titanium alloy plates
Magnetic force microscopy of epitaxial Fe2CoAl and Co2FeAl Heusler alloy films and microstructures
Research supported by RFBR grant 17-57-45024 IND-a
Fusion and singular vectors in A1{(1)} highest weight cyclic modules
We show how the interplay between the fusion formalism of conformal field
theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for
the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page
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