870 research outputs found
On centralizer algebras for spin representations
We give a presentation of the centralizer algebras for tensor products of
spinor representations of quantum groups via generators and relations. In the
even-dimensional case, this can be described in terms of non-standard
q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a
certain subalgebra will appear. In the classical case q = 1 the relations boil
down to Lie algebra relations
Two-Rowed Hecke Algebra Representations at Roots of Unity
In this paper, we initiate a study into the explicit construction of
irreducible representations of the Hecke algebra of type in
the non-generic case where is a root of unity. The approach is via the
Specht modules of which are irreducible in the generic case, and
possess a natural basis indexed by Young tableaux. The general framework in
which the irreducible non-generic -modules are to be constructed is set
up and, in particular, the full set of modules corresponding to two-part
partitions is described. Plentiful examples are given.Comment: LaTeX, 9 pages. Submitted for the Proceedings of the 4th
International Colloquium ``Quantum Groups and Integrable Systems,'' Prague,
22-24 June 199
Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras
A construction of bases for cell modules of the Birman--Murakami--Wenzl (or
B--M--W) algebra by lifting bases for cell modules of
is given. By iterating this procedure, we produce cellular bases for B--M--W
algebras on which a large abelian subalgebra, generated by elements which
generalise the Jucys--Murphy elements from the representation theory of the
Iwahori--Hecke algebra of the symmetric group, acts triangularly. The
triangular action of this abelian subalgebra is used to provide explicit
criteria, in terms of the defining parameters and , for B--M--W algebras
to be semisimple. The aforementioned constructions provide generalisations, to
the algebras under consideration here, of certain results from the Specht
module theory of the Iwahori--Hecke algebra of the symmetric group
Quantum Gravity and the Algebra of Tangles
In Rovelli and Smolin's loop representation of nonperturbative quantum
gravity in 4 dimensions, there is a space of solutions to the Hamiltonian
constraint having as a basis isotopy classes of links in R^3. The physically
correct inner product on this space of states is not yet known, or in other
words, the *-algebra structure of the algebra of observables has not been
determined. In order to approach this problem, we consider a larger space H of
solutions of the Hamiltonian constraint, which has as a basis isotopy classes
of tangles. A certain algebra T, the ``tangle algebra,'' acts as operators on
H. The ``empty state'', corresponding to the class of the empty tangle, is
conjectured to be a cyclic vector for T. We construct simpler representations
of T as quotients of H by the skein relations for the HOMFLY polynomial, and
calculate a *-algebra structure for T using these representations. We use this
to determine the inner product of certain states of quantum gravity associated
to the Jones polynomial (or more precisely, Kauffman bracket).Comment: 16 pages (with major corrections
Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
We construct an explicit isomorphism between blocks of cyclotomic Hecke
algebras and (sign-modified) Khovanov-Lauda algebras in type A. These
isomorphisms connect the categorification conjecture of Khovanov and Lauda to
Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally
graded, which allows us to exhibit a non-trivial Z-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive
characteristic.Comment: 32 pages; minor changes to section
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
Integrability in anyonic quantum spin chains via a composite height model
Recently, properties of collective states of interacting non-abelian anyons
have attracted a considerable attention. We study an extension of the `golden
chain model', where two- and three-body interactions are competing. Upon
fine-tuning the interaction, the model is integrable. This provides an
additional integrable point of the model, on top of the integrable point, when
the three-body interaction is absent. To solve the model, we construct a new,
integrable height model, in the spirit of the restricted solid-on-solid model
solved by Andrews, Baxter and Forrester. The heights in our model live on both
the sites and links of the square lattice. The model is solved by means of the
corner transfer matrix method. We find a connection between local height
probabilities and characters of a conformal field theory governing the critical
properties at the integrable point. In the antiferromagnetic regime, the
criticality is described by the Z_k parafermion conformal field theory, while
the su(2)_1 x su(2)_1 x su(2)_(k-2) / su(2)_k coset conformal field theory
describes the ferromagnetic regime.Comment: 31 pages; v2: minor change
Inflammation in Metabolic Cardiomyopathy
Overlapping pandemics of lifestyle-related diseases pose a substantial threat to cardiovascular health. Apart from coronary artery disease, metabolic disturbances linked to obesity, insulin resistance and diabetes directly compromise myocardial structure and function through independent and shared mechanisms heavily involving inflammatory signals. Accumulating evidence indicates that metabolic dysregulation causes systemic inflammation, which in turn aggravates cardiovascular disease. Indeed, elevated systemic levels of pro-inflammatory cytokines and metabolic substrates induce an inflammatory state in different cardiac cells and lead to subcellular alterations thereby promoting maladaptive myocardial remodeling. At the cellular level, inflammation-induced oxidative stress, mitochondrial dysfunction, impaired calcium handling, and lipotoxicity contribute to cardiomyocyte hypertrophy and dysfunction, extracellular matrix accumulation and microvascular disease. In cardiometabolic patients, myocardial inflammation is maintained by innate immune cell activation mediated by pattern recognition receptors such as Toll-like receptor 4 (TLR4) and downstream activation of the NLRP3 inflammasome and NF-κB-dependent pathways. Chronic low-grade inflammation progressively alters metabolic processes in the heart, leading to a metabolic cardiomyopathy (MC) phenotype and eventually to heart failure with preserved ejection fraction (HFpEF). In accordance with preclinical data, observational studies consistently showed increased inflammatory markers and cardiometabolic features in patients with HFpEF. Future treatment approaches of MC may target inflammatory mediators as they are closely intertwined with cardiac nutrient metabolism. Here, we review current evidence on inflammatory processes involved in the development of MC and provide an overview of nutrient and cytokine-driven pro-inflammatory effects stratified by cell type
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