845 research outputs found
Cellular structure of -Brauer algebras
In this paper we consider the -Brauer algebra over a commutative
noetherian domain. We first construct a new basis for -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 Moreover, when is a field of
arbitrary characteristic, we determine for which parameters the -Brauer
algebras are quasi-heredity. So the general theory of cellular algebras and
quasi-hereditary algebras applies to -Brauer algebras. As a consequence, we
can determine all irreducible representations of -Brauer algebras by linear
algebra methods
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
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
Topological Quantum Field Theories and Operator Algebras
We review "quantum" invariants of closed oriented 3-dimensional manifolds
arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory
and Noncommutative Geometry", Sendai, November 200
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
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
On the Representation Theory of an Algebra of Braids and Ties
We consider the algebra introduced by F. Aicardi and J.
Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor
space representation for and show that this is faithful. We use
it to give a basis for and to classify its irreducible
representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic
Combinatorics
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
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