Following V. Toledano-Laredo and S. Gautam approach we construct isomorphism between super $\hbar$-Yangian $Y_{\hbar}(A(m,n))$ of special linear superalgebra and quantum loop superalgebra $U_{\hbar}(LA(m,n))$.
Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized Weyl algebras at roots of unity.
We show that a finitely strongly generated, non-negatively graded vertex algebra $V$ is $C_2$-cofinite if and only if it is lisse in the sense of Beilinson, Feigin and Mazur. This shows that the $C_2$-cofiniteness is indeed a natural finiteness condition.
We determine a set of primitive idempotents and the basic algebra of the restricted quantum group $\bar{U}_qsl_2(\mathbb{C})$. As a result, we can show the dimension of the space of symmetric linear functions of $\bar{U}_qsl_2(\mathbb{C})$ is $3p-1$
Let $H$ be a character Hopf algebra. Every right coideal subalgebra that contains the coradical has a PBW-basis which can be extended up to a PBW-basis of $H.$
Abstract The "Qa-m9" specificity has been defined by a monoclonal antibody, and evidence for three-gene control of its expression has been demonstrated. The Qa allocation was made on the basis of H-2 linkage (H-2 congenic strains, Rl lines), differential reaction with B6.K1 and B6.K2, and biochemical analysis (two chains: 39,000 Mr and 12,000 Mr). "Qa-m9" is expressed on T and B cells in spleen and lymph node; it is present on a small population of bone marrow cells but is absent from thymocytes. The three genes involved in the expression of the antigen are: a) an H-2 linked Qa gene (possibly encoded by a gene different from Qa-2-6); b) an H-3 linked gene--probably beta 2m; and c) an H-2D linked gene that controls the amount of antigen present. It is likely that the determinant is of the "combinatorial" or conformational type, whereby the C57BL/6-type Qa heavy chain and the appropriate beta 2m light chain must both be in association. Thus, the study provides evidence for a multi-gene control of antigen expression and demonstrates the potential for generating new antigens with diversity at a post-translational level.
ABSTRACT The qa-3 gene, one of the four genes in the qa gene cluster, encodes quinate (shikimate) dehydrogenase (quinate: NAD oxidoreductase, ER 1.1.1.24), the first enzyme in the inducible quinic acid catabolic pathway in Neurospora crassa. Genetic analyses have localized 26 qa-3 mutants at 11 sites on the qa-3 genetic map on the basis of prototroph frequencies. Certain mutants, e.g., 336-3-10 and 336-3-3, are located at opposite ends of the qa-3 gene. Data from four-point crosses (qa-1S mutant 124 x five different qa-3 mutants in triple mutants qa-3, qa-4, qa-2) indicate the following orientation of the qa-3 gene within the qa cluster: qa-1, qa-3 mutant 336-3-10 ("left" end) qa-3 mutant 336-3-3 ("right" end), qa-4, qa-2. Ultraviolet-induced revertants have been obtained from 14 of the qa-3 mutants. The revertable mutants fall into two major classes: those that revert by changes either at the same site or at a second site within the qa-3 gene, and those that revert by unlinked suppressor mutations. The intragenic revertants can be further distinguished by quantative and/or qualitative differences in their quinate dehydrogenase activities. Some revertants with activities either equivalent to or less than wild type produce a thermostable enzyme, and others an enzyme which is thermolabile in vitro at 35°. A concentration of quinic acid or shikimic acid as low as 50 μm protects the enzyme markedly from heat inactivation. The genetic organization and the orientation of the qa-3 gene are discussed with respect to its direction of transcription and to the possible localization of a promoter (initiator) region(s) within the qa gene cluster.
Abstract Two-dimensional polyacrylamide gel electrophoresis (2-D PAGE) was used to examine and compare the products of the Qa-1 locus. Analysis of Qa-1 isolated from detergent lysates of surface labeled cells indicated this molecule was a slightly acidic 48,000 to 50,000 dalton glycoprotein that displayed little charge heterogeneity on resting lymphocytes. The level of expression and degree of charge heterogeneity were both increased on activated lymphocytes. Direct comparison of the Qa-1b, Qa-1c, and Qa-1d allelic products by 2-D PAGE revealed that these three molecules could be distinguished from one another on the basis of isoelectric point, indicating that they were distinct at the molecular level. Comparison of Qa-1 isolated from several Qa-1b strains did not detect additional polymorphism. Removal of asparagine-linked oligosaccharides by treatment with endoglycosidase F indicated that carbohydrate contributed 10,000 to 12,000 to the m.w. of these allelic products. Comparative 2-D PAGE analysis could not distinguish between the deglycosylated Qa-1b, Qa-1c, and Qa-1d allelic products, implying that these molecules have similar primary structures. Peptide mapping supported this conclusion. Proteolytic digestion of the deglycosylated Qa-1b and Qa-1c allelic products resulted in identical peptide map patterns; such treatment of the deglycosylated Qa-1d allelic product produced a slightly different pattern. Peptide mapping analysis also demonstrated that the Tlaa and Qa-1a allelic products were distinct from one another, as well as being very different from the other three Qa-1 allelic products.
We use one-dimensional double affine Hecke algebras to introduce q-counterparts of the Gauss integrals and new types of Gauss-Selberg sums at roots of unity.
In this paper it is shown that every irreducible vertex algebra of countable dimension and every simple vertex operator algebra are nondegenerate in the sense of Etingof and Kazhdan.
The idea that a Dynkin diagram can provide one of the `spatial' variables for an integrable difference-difference system is no news. I propose a `model' where the only variable is of this sort.
A criterion for comonadicity of the extension-of- scalars functor associated to an extension of (not necessarily commutative) rings is given. As an application of this criterion, some known results on the comonadicity of such functors are obtained.