766 research outputs found
Integrality of Homfly (1,1)-tangle invariants
Given an invariant J(K) of a knot K, the corresponding (1,1)-tangle invariant
J'(K)=J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the
unknot U.
We prove here that J' is always an integer 2-variable Laurent polynomial when
J is the Homfly satellite invariant determined by decorating K with any
eigenvector of the meridian map in the Homfly skein of the annulus.
Specialisation of the 2-variable polynomials for suitable choices of
eigenvector shows that the (1,1)-tangle irreducible quantum sl(N) invariants of
K are integer 1-variable Laurent polynomials.Comment: 10 pages, including several interspersed figure
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
Generalized negligible morphisms and their tensor ideals
We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category over a local ring . If the maximal ideal of is generated by a single element, we show that any thick ideal of admits an explicitely given modified trace function. As examples we consider various Deligne categories and the categories of tilting modules for a quantum group at a root of unity and for a semisimple, simply connected algebraic group in prime characteristic. We prove an elementary geometric description of the thick ideals in quantum type A and propose a similar one in the modular case
Braid rigidity for path algebras
Path algebras are a convenient way of describing decompositions of tensor powers of an object in a tensor category. If the category is braided, one obtains representations of the braid groups for all . We say that such representations are rigid if they are determined by the path algebra and the representations of . We show that besides the known classical cases also the braid representations for the path algebra for the 7-dimensional representation of satisfies the rigidity condition, provided generates \End(V^{\otimes 3}). We obtain a complete classification of ribbon tensor categories with the fusion rules of \g(G_2) if this condition is satisfied
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
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
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
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
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.
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