105 research outputs found
A p-Adic Model of DNA Sequence and Genetic Code
Using basic properties of p-adic numbers, we consider a simple new approach
to describe main aspects of DNA sequence and genetic code. Central role in our
investigation plays an ultrametric p-adic information space which basic
elements are nucleotides, codons and genes. We show that a 5-adic model is
appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance,
is also suitable for genetic code and for a more advanced employment in
genomics. We find that genetic code degeneracy is related to the p-adic
distance between codons.Comment: 13 pages, 2 table
R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
We review some of the strategies that can be implemented to infer an
-matrix from the knowledge of its Hamiltonian. We apply them to the
classification achieved in arXiv:1306.6303, on three state -invariant
Hamiltonians solvable by CBA, focusing on models for which the -matrix is
not trivial.
For the 19-vertex solutions, we recover the -matrices of the well-known
Zamolodchikov--Fateev and Izergin--Korepin models. We point out that the
generalized Bariev Hamiltonian is related to both main and special branches
studied by Martins in arXiv:1303.4010, that we prove to generate the same
Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we
are able to state some no-go theorems on its -matrix.
For 17-vertex Hamiltonians, we produce a new -matrix.Comment: 22 page
W-superalgebras as truncation of super-Yangians
We show that some finite W-superalgebras based on gl(M|N) are truncation of
the super-Yangian Y(gl(M|N)). In the same way, we prove that finite
W-superalgebras based on osp(M|2n) are truncation of the twisted super-Yangians
Y(gl(M|2n))^{+}.
Using this homomorphism, we present these W-superalgebras in an R-matrix
formalism, and we classify their finite-dimensional irreducible
representations.Comment: Latex, 32 page
Development of a unified tensor calculus for the exceptional Lie algebras
The uniformity of the decomposition law, for a family F of Lie algebras which
includes the exceptional Lie algebras, of the tensor powers ad^n of their
adjoint representations ad is now well-known. This paper uses it to embark on
the development of a unified tensor calculus for the exceptional Lie algebras.
It deals explicitly with all the tensors that arise at the n=2 stage, obtaining
a large body of systematic information about their properties and identities
satisfied by them. Some results at the n=3 level are obtained, including a
simple derivation of the the dimension and Casimir eigenvalue data for all the
constituents of ad^3. This is vital input data for treating the set of all
tensors that enter the picture at the n=3 level, following a path already known
to be viable for a_1. The special way in which the Lie algebra d_4 conforms to
its place in the family F alongside the exceptional Lie algebras is described.Comment: 27 pages, LaTeX 2
Duality and Representations for New Exotic Bialgebras
We find the exotic matrix bialgebras which correspond to the two
non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta,
namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14
which are not deformations of the of the classical algebras of functions on
GL(2) or GL(1|1). With this we finalize the classification of the matrix
bialgebras which unital associative algebras generated by four elements. We
also find the corresponding dual bialgebras of these new exotic bialgebras and
study their representation theory in detail. We also discuss in detail a
special case of R_{S1,4} in which the corresponding algebra turns out to be a
special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn;
reference updated; v3: corrections in subsection 3.
On the Fairlie's Moyal formulation of M(atrix)- theory
Starting from the Moyal formulation of M-theory in the large N-limit, we
propose to reexamine the associated membrane equations of motion in 10
dimensions formulated in terms of Poisson bracket. Among the results obtained,
we rewrite the coupled first order Nahm's equations into a simple form leading
in turn to their systematic relation with Yang Mills equations of
motion. The former are interpreted as the vanishing condition of some conserved
currents which we propose. We develop also an algebraic analysis in which an
ansatz is considered and find an explicit form for the membrane solution of our
problem. Typical solutions known in literature can also emerge as special cases
of the proposed solutionComment: 16 page
Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator
The uniformity, for the family of exceptional Lie algebras g, of the
decompositions of the powers of their adjoint representations is well-known now
for powers up to the fourth. The paper describes an extension of this
uniformity for the totally antisymmetrised n-th powers up to n=9, identifying
(see Tables 3 and 6) families of representations with integer eigenvalues
5,...,9 for the quadratic Casimir operator, in each case providing a formula
(see eq. (11) to (15)) for the dimensions of the representations in the family
as a function of D=dim g. This generalises previous results for powers j and
Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the
dimension formulas are discussed and the possibility that they may be valid for
a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos
correcte
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio
Strings from Gauged Wess-Zumino-Witten Models
We present an algebraic approach to string theory. An embedding of
in a super Lie algebra together with a grading on the Lie algebra determines a
nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra
in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of
the Wess-Zumino-Witten model to some extension of the superconformal
algebra. The extension is completely determined by the embedding. The
realization of the superconformal algebra is determined by the grading. For a
particular choice of grading, one obtains in this way, after twisting, the BRST
structure of a string theory. We classify all embeddings of into Lie
super algebras and give a detailed account of the branching of the adjoint
representation. This provides an exhaustive classification and characterization
of both all extended superconformal algebras and all string theories
which can be obtained in this way.Comment: 50 pages, LaTe
The Morphology of N=6 Chern-Simons Theory
We tabulate various properties of the language of N=6 Chern-Simons Theory, in
the sense of Polyakov. Specifically we enumerate and compute character formulas
for all syllables of up to four letters, i.e. all irreducible representations
of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We
also present all tensor product decompositions for up to four singletons and
list the (cyclically invariant) four-letter words, which correspond to
single-trace operators of length four. As an application of these results we
use the two-loop dilatation operator to compute the leading correction to the
Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.Comment: 41 pages, 1 figure; v2: minor correction
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