Cellular structure of qq-Brauer algebras

In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense of Graham and Lehrer. In particular, they are shown to be an iterated inflation of Hecke algebras of type $A_{n-1}.$ Moreover, when $R$ is a field of arbitrary characteristic, we determine for which parameters the $q$-Brauer algebras are quasi-heredity. So the general theory of cellular algebras and quasi-hereditary algebras applies to $q$-Brauer algebras. As a consequence, we can determine all irreducible representations of $q$-Brauer algebras by linear algebra methods

Early functional results after Hemiarthroplasty for femoral neck fracture: a randomized comparison between a minimal invasive and a conventional approach

BACKGROUND: A minimal invasive approach for elective hip surgery has been implemented in our institution in the past. It is widely hypothesized that implanting artificial hips in a minimal invasive fashion decreases surgical trauma and is helpful in the rehabilitation process in elective hip surgery. Thereby geriatric patients requiring emergency hip surgery also could theoretically benefit from a procedure that involves less tissue trauma. METHODS: Sixty patients who sustained a fractured neck of femur were randomly assigned into two groups. In the minimal invasive arm, the so called “direct anterior approach” (DAA) was chosen, in the conventional arm the Watson-Jones-Approach was used for implantation of a bipolar hemi-arthroplasty. Primary outcome parameter was the mobility as measured by the four-item-Barthel index. Secondary outcome parameters included pain, haemoglobin-levels, complications, duration of surgery, administration of blood transfusion and external length of incision. Radiographs were evaluated. RESULTS: A statistically significant difference (p = 0,009) regarding the mobility as measured with the four-item Barthel index was found at the 5th postoperative day, favouring the DAA. Evaluation of the intensity of pain with a visual analogue scale (VAS) showed a statistically significant difference (p = 0,035) at day 16. No difference was evident in the comparison of radiographic results. CONCLUSIONS: Comparing two different approaches to the hip joint for the implantation of a bipolar hemi-arthroplasty after fractured neck of femur, it can be stated that mobilization status is improved for the DAA compared to the WJA when measured by the four-item Barthel index, there is less pain as measured using the VAS. There is no radiographic evidence that a minimal invasive technique leads to inferior implant position. Level of Evidence: Level II therapeutic study

Characteristic Relations for Quantum Matrices

General algebraic properties of the algebras of vector fields over quantum linear groups $GL_q(N)$ and $SL_q(N)$ are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum analogues of the characteristic polynomial and characteristic identity are obtained for them. The $q$-analogues of the Newton relations connecting two different generating sets of central elements of these algebras (the determinant-like and the trace-like ones) are derived. This allows one to express the $q$-determinant of quantized vector fields in terms of their $q$-traces.Comment: 11 pages, latex, an important reference [16] added

Mapping spot blotch resistance genes in four barley populations

Bipolaris sorokiniana (teleomorph: Cochliobolus sativus) is the fungal pathogen responsible for spot blotch in barley (Hordeum vulgare L.) and occurs worldwide in warmer, humid growing conditions. Current Australian barley varieties are largely susceptible to this disease and attempts are being made to introduce sources of resistance from North America. In this study we have compared chromosomal locations of spot blotch resistance reactions in four North American two-rowed barley lines; the North Dakota lines ND11231-12 and ND11231-11 and the Canadian lines TR251 and WPG8412-9-2-1. Diversity Arrays Technology (DArT)-based PCR, expressed sequence tag (EST) and SSR markers have been mapped across four populations derived from crosses between susceptible parental lines and these four resistant parents to determine the location of resistance loci. Quantitative trait loci (QTL) conferring resistance to spot blotch in adult plants (APR) were detected on chromosomes 3HS and 7HS. In contrast, seedling resistance (SLR) was controlled solely by a locus on chromosome 7HS. The phenotypic variance explained by the APR QTL on 3HS was between 16 and 25% and the phenotypic variance explained by the 7HS APR QTL was between 8 and 42% across the four populations. The SLR QTL on 7HS explained between 52 to 64% of the phenotypic variance. An examination of the pedigrees of these resistance sources supports the common identity of resistance in these lines and indicates that only a limited number of major resistance loci are available in current two-rowed germplasm

Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Development of a genetic linkage map for Sharon goatgrass (Aegilops sharonensis) and mapping of a leaf rust resistance gene

Aegilops sharonensis (Sharon goatgrass), a diploid wheat relative, is known to be a rich source of disease resistance genes for wheat improvement. To facilitate the transfer of these genes into wheat, information on their chromosomal location is important. A genetic linkage map of Ae. sharonensis was constructed based on 179 F2 plants derived from a cross between accessions resistant (1644) and susceptible (1193) to wheat leaf rust. The linkage map was based on 389 markers (377 Diversity Arrays Technology (DArT) and 12 simple sequence repeat (SSR) loci) and was comprised of 10 linkage groups, ranging from 2.3 to 124.6 cM. The total genetic length of the map was 818.0 cM, with an average interval distance between markers of 3.63 cM. Based on the chromosomal location of 115 markers previously mapped in wheat, the four linkage groups of A, B, C, and E were assigned to Ae. sharonensis (Ssh) and homoeologous wheat chromosomes 6, 1, 3, and 2. The single dominant gene (designated LrAeSh1644) conferring resistance to leaf rust race THBJ in accession 1644 was positioned on linkage group A (chromosome 6Ssh) and was flanked by DArT markers wpt-9881 (at 1.9 cM distal from the gene) and wpt-6925 (4.5 cM proximal). This study clearly demonstrates the utility of DArT for genotyping uncharacterized species and tagging resistance genes where pertinent genomic information is lacking

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454