701 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
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
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
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
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.
The growth of ZnO crystals from the melt
The peculiar properties of zinc oxide (ZnO) make this material interesting
for very different applications like light emitting diodes, lasers, and
piezoelectric transducers. Most of these applications are based on epitaxial
ZnO layers grown on suitable substrates, preferably bulk ZnO. Unfortunately the
thermochemical properties of ZnO make the growth of single crystals difficult:
the triple point 1975 deg C., 1.06 bar and the high oxygen fugacity at the
melting point p_O2 = 0.35 bar lead to the prevailing opinion that ZnO crystals
for technical applications can only be grown either by a hydrothermal method or
from "cold crucibles" of solid ZnO. Both methods are known to have significant
drawbacks. Our thermodynamic calculations and crystal growth experiments show,
that in contrast to widely accepted assumptions, ZnO can be molten in metallic
crucibles, if an atmosphere with "self adjusting" p_O2 is used. This new result
is believed to offer new perspectives for ZnO crystal growth by established
standard techniques like the Bridgman method.Comment: 6 pages, 6 figures, accepted for J. Crystal Growt
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
- …