Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.Comment: 21page

Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A(1)((1))

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A(1)((1)). A realization of the basic representation that is of "D-2((2))"-type plays the central role

Compound basis arising from the basic A1(1)A^{(1)}_{1}-module

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.Comment: 12 page

Heme-dependent autophosphorylation of a heme sensor kinase, ChrS, from Corynebacterium diphtheriae reconstituted in proteoliposomes

AbstractCorynebacterium diphteriae employs the response regulator, ChrA, and the sensor kinase, ChrS, of a two-component signal transduction system to utilize host heme iron. Although ChrS is predicted to encode a heme sensor, the sensing mechanism remains to be characterized. In this report, ChrS expressed in Eshcherichia coli membranes was solubilized and purified using decylmaltoside. ChrS protein incorporated into proteoliposomes catalyzed heme-dependent autophosphorylation by ATP. Other metalloporphyrins and iron did not stimulate kinase activity. The UV–Vis spectrum of hemin in the ChrS–proteoliposomes indicated that heme directly interacts with ChrS. This is the first functional reconstitution of a bacterial heme-sensing protein

Spectropolarimetric Evidence for Radiatively Inefficient Accretion in an Optically Dull Active Galaxy

We present Subaru/FOCAS spectropolarimetry of two active galaxies in the Cosmic Evolution Survey. These objects were selected to be optically dull, with the bright X-ray emission of an AGN but missing optical emission lines in our previous spectroscopy. Our new observations show that one target has very weak emission lines consistent with an optically dull AGN, while the other object has strong emission lines typical of a host-diluted Type 2 Seyfert galaxy. In neither source do we observe polarized emission lines, with 3-sigma upper limits of P_BLR < 2%. This means that the missing broad emission lines (and weaker narrow emission lines) are not due to simple anisotropic obscuration, e.g., by the canonical AGN torus. The weak-lined optically dull AGN exhibits a blue polarized continuum with P = 0.78 +/- 0.07% at 4400 A < lambda_rest < 7200 A (P = 1.37 +/- 0.16% at 4400 A < lambda_rest < 5050 A). The wavelength dependence of this polarized flux is similar to that of an unobscured AGN continuum and represents the intrinsic AGN emission, either as synchrotron emission or the outer part of an accretion disk reflected by a clumpy dust scatterer. Because this intrinsic AGN emission lacks emission lines, this source is likely to have a radiatively inefficient accretion flow.Comment: Accepted to ApJ. 6 pages, 2 figure