Solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded modules

We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- \gtsl_{n+1}-modules. The formulas are closely related to WZNW model at a rational level.Comment: 13 page

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 $q-$connection with coefficients in a ring of skew polynomials and study the structure of quantum group modules twisted by a $q-$connection.Comment: 25 page

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

New Data on Comparative Cytogenetics of the Mouse-Like Hamsters (Calomyscus Thomas, 1905) from Iran and Turkmenistan.

The taxonomy of the genus Calomyscus remains controversial. According to the latest systematics the genus includes eight species with great karyotypic variation. Here, we studied karyotypes of 14 Calomyscus individuals from different regions of Iran and Turkmenistan using a new set of chromosome painting probes from a Calomyscus sp. male (2n = 46, XY; Shahr-e-Kord-Soreshjan-Cheshme Maiak Province). We showed the retention of large syntenic blocks in karyotypes of individuals with identical chromosome numbers. The only rearrangement (fusion 2/21) differentiated Calomyscus elburzensis, Calomyscus mystax mystax, and Calomyscus sp. from Isfahan Province with 2n = 44 from karyotypes of C. bailwardi, Calomyscus sp. from Shahr-e-Kord, Chahar Mahal and Bakhtiari-Aloni, and Khuzestan-Izeh Provinces with 2n = 46. The individuals from Shahdad tunnel, Kerman Province with 2n = 51-52 demonstrated non-centric fissions of chromosomes 4, 5, and 6 of the 46-chromosomal form with the formation of separate small acrocentrics. A heteromorphic pair of chromosomes in a specimen with 2n = 51 resulted from a fusion of two autosomes. C-banding and chromomycin A3-DAPI staining after G-banding showed extensive heterochromatin variation between individuals