864 research outputs found
A Tensor Product Theorem Related To Perfect Crystals
Kang et al. provided a path realization of the crystal graph of a highest
weight module over a quantum affine algebra, as certain semi-infinite tensor
products of a single perfect crystal. In this paper, this result is generalized
to give a realization of the tensor product of several highest weight modules.
The underlying building blocks of the paths are finite tensor products of
several perfect crystals. The motivation for this work is an interpretation of
fermionic formulas, which arise from the combinatorics of Bethe Ansatz studies
of solvable lattice models, as branching functions of affine Lie algebras. It
is shown that the conditions for the tensor product theorem are satisfied for
coherent families of crystals previously studied by Kang, Kashiwara and Misra,
and the coherent family of crystals of type .Comment: 27 pages; error correcte
Virtual crystals and Kleber's algorithm
Kirillov and Reshetikhin conjectured what is now known as the fermionic
formula for the decomposition of tensor products of certain finite dimensional
modules over quantum affine algebras. This formula can also be extended to the
case of -deformations of tensor product multiplicities as recently
conjectured by Hatayama et al. (math.QA/9812022 and math.QA/0102113). In its
original formulation it is difficult to compute the fermionic formula
efficiently. Kleber (q-alg/9611032 and math.QA/9809087) found an algorithm for
the simply-laced algebras which overcomes this problem. We present a method
which reduces all other cases to the simply-laced case using embeddings of
affine algebras. This is the fermionic analogue of the virtual crystal
construction by the authors, which is the realization of crystal graphs for
arbitrary quantum affine algebras in terms of those of simply-laced type.Comment: 23 pages; style file youngtab.sty required, package pstricks
required; fixed typo in Eq. (5.2
A crystal to rigged configuration bijection for nonexceptional affine algebras
Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight
vectors in the crystal graph of a tensor power of the vector representation,
and combinatorial objects called rigged configurations, for type .
We define an analogous bijection for all nonexceptional affine types, thereby
proving (in this special case) the fermionic formulas conjectured by Hatayama,
Kuniba, Takagi, Tsuboi, Yamada, and the first author.Comment: 34 pages; axodraw.sty file require
Application of a small oscillating magnetic field to reveal the peak effect in the resistivity of Nb3Sn
By the application of a small oscillating magnetic field parallel to the main
magnetic field and perpendicular to the transport current, we were able to
unveil the peak effect in the resistivity data of NbSn near the upper
critical field . We investigated the dependence of this effect on the
frequency and the amplitude of the oscillating magnetic field and show that the
used technique can be more sensitive to detect the peak effect in a certain
range of temperatures and magnetic fields than conventional magnetization
measurements.Comment: 17 pages, 10 figure
Crystal bases and q-identities
The relation of crystal bases with -identities is discussed, and some new
results on crystals and -identities associated with the affine Lie algebra
are presented.Comment: 25 pages, style file axodraw.sty require
A bijection between Littlewood-Richardson tableaux and rigged configurations
A bijection is defined from Littlewood-Richardson tableaux to rigged
configurations. It is shown that this map preserves the appropriate statistics,
thereby proving a quasi-particle expression for the generalized Kostka
polynomials, which are q-analogues of multiplicities in tensor products of
irreducible general linear group modules indexed by rectangular partitions.Comment: 66 pages, AMS-LaTeX, requires xy.sty and related file
- …