696 research outputs found
Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
This paper continues the project of constructing the character formulae for
the positive energy unitary irreducible representations of the N-extended D=4
conformal superalgebras su(2,2/N). In the first paper we gave the bare
characters which represent the defining odd entries of the characters. Now we
give the full explicit character formulae for N=1 and for several important
examples for N=2 and N=4.Comment: 48 pages, TeX with Harvmac, overlap in preliminaries with
arXiv:hep-th/0406154; some comments and references adde
Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,
A new approach to the theory of polynomial solutions of q - difference
equations is proposed. The approach is based on the representation theory of
simple Lie algebras and their q - deformations and is presented here for
U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of
n(n-1)/2 commuting variables and depending on n-1 complex representation
parameters r_i, is constructed. From this realization lowest weight modules
(LWM) are obtained which are studied in detail for the case n=3 (the well known
n=2 case is also recovered). All reducible LWM are found and the polynomial
bases of their invariant irreducible subrepresentations are explicitly given.
This also gives a classification of the quasi-exactly solvable operators in the
present setting. The invariant subspaces are obtained as solutions of certain
invariant q - difference equations, i.e., these are kernels of invariant q -
difference operators, which are also explicitly given. Such operators were not
used until now in the theory of polynomial solutions. Finally the states in all
subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files
Invariant Differential Operators and Characters of the AdS_4 Algebra
The aim of this paper is to apply systematically to AdS_4 some modern tools
in the representation theory of Lie algebras which are easily generalised to
the supersymmetric and quantum group settings and necessary for applications to
string theory and integrable models. Here we introduce the necessary
representations of the AdS_4 algebra and group. We give explicitly all singular
(null) vectors of the reducible AdS_4 Verma modules. These are used to obtain
the AdS_4 invariant differential operators. Using this we display a new
structure - a diagram involving four partially equivalent reducible
representations one of which contains all finite-dimensional irreps of the
AdS_4 algebra. We study in more detail the cases involving UIRs, in particular,
the Di and the Rac singletons, and the massless UIRs. In the massless case we
discover the structure of sets of 2s_0-1 conserved currents for each spin s_0
UIR, s_0=1,3/2,... All massless cases are contained in a one-parameter
subfamily of the quartet diagrams mentioned above, the parameter being the spin
s_0. Further we give the classification of the so(5,C) irreps presented in a
diagramatic way which makes easy the derivation of all character formulae. The
paper concludes with a speculation on the possible applications of the
character formulae to integrable models.Comment: 30 pages, 4 figures, TEX-harvmac with input files: amssym.def,
amssym.tex, epsf.tex; version 2 1 reference added; v3: minor corrections;
v.4: minor corrections, v.5: minor corrections to conform with version in J.
Phys. A: Math. Gen; v.6.: small correction and addition in subsections 4.1 &
4.
Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R)
We give the classification of the positive energy (lowest weight) unitary
irreducible representations of the superalgebras osp(1|2n,R).Comment: 20 pages, LATEX2e (revtex4,amsmath,amssymb), Plenary talk by VKD at X
International Conference on Symmetry Methods in Physics, Yerevan,
13-21.8.2003; added acknowledgements; corrected misprint
Anti de Sitter Holography via Sekiguchi Decomposition
In the present paper we start consideration of anti de Sitter holography in
the general case of the (q+1)-dimensional anti de Sitter bulk with boundary
q-dimensional Minkowski space-time. We present the group-theoretic foundations
that are necessary in our approach. Comparing what is done for q=3 the new
element in the present paper is the presentation of the bulk space as the
homogeneous space G/H = SO(q,2)/SO(q,1), which homogeneous space was studied by
Sekiguchi.Comment: 10 pages, to appear in the Proceedings of the XI International
Workshop "Lie Theory and Its Applications in Physics", (Varna, Bulgaria, June
2015
Positive Energy Representations, Holomorphic Discrete Series and Finite-Dimensional Irreps
Let G be a semi-simple non-compact Lie group with unitary lowest/highest
weight representations. We consider explicitly the relation between three types
of representations of G: positive energy (unitary lowest
weight)representations, (holomorphic) discrete series representations and
non-unitary finite-dimensional irreps. We consider mainly the conformal groups
SO(n,2) treating in full detail the cases n=1,3,4.Comment: 28 pages, TEX with Harvmac using amssym.def, amssym.tex, epsf.tex;
v2: new texts in Sections 1 & 3, new refs; v3: added 5 figures; v4: small
correction
Group-Theoretical Classification of BPS States in D=4 Conformal Supersymmetry: the Case of (1/N)-BPS
In an earlier paper we gave the complete group-theoretical classification of
BPS states of the N-extended D=4 conformal superalgebras su(2,2/N), but not all
interesting cases were given in detail. In the present paper we spell out the
interesting case of (1/N)-BPS and possibly protected states.Comment: LATEX2e, 8 pages, Plenary talk at the International Workshop
'Supersymmetries and Quantum Symmetries', Dubna, 18-23.7.2011, to appear in
the Proceedings, editors Evgeny Ivanov et a
Representations of the Generalized Lie Algebra sl(2)_q
We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra \ssll (2)_q introduced by
Lyubashenko and the second named author. We consider separately the cases of
generic and at roots of unity. Some of the representations have no
classical analog even for generic . Some of the representations have no
analog to the finite-dimensional representations of the quantised enveloping
algebra , while in those that do there are different matrix
elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de
A family of solvable non-rational conformal field theories
We find non-rational conformal field theories in two dimensions, which are
solvable due to their correlators being related to correlators of Liouville
theory. Their symmetry algebra consists of the dimension-two stress-energy
tensor, and two dimension-one fields. The theories come in a family with two
parameters: the central charge c and a complex number m. The special case m=0
corresponds to Liouville theory (plus two free bosons), and m=1 corresponds to
the H3+ model. In the case m=2 we show that the correlators obey third-order
differential equations, which are associated to a subsingular vector of the
symmetry algebra.Comment: 14 pages, v2: role of subsingular vectors clarifie
Accurate three states model for amino acids with two chemically coupled titrating sites in explicit solvent atomistic constant pH simulations and pK<sub>a</sub> calculations.
Correct protonation of titratable groups in biomolecules is crucial for their accurate description by molecular dynamics simulations. In the context of constant pH simulations, an additional protonation degree of freedom is introduced for each titratable site, allowing the protonation state to change dynamically with changing structure or electrostatics. Here, we extend previous approaches for an accurate description of chemically coupled titrating sites. A second reaction coordinate is used to switch between two tautomeric states of an amino acid with chemically coupled titratable sites, such as aspartate (Asp), glutamate (Glu), and histidine (His). To this aim, we test a scheme involving three protonation states. To facilitate charge neutrality as required for periodic boundary conditions and Particle Mesh Ewald (PME) electrostatics, titration of each respective amino acid is coupled to a “water” molecule that is charged in the opposite direction. Additionally, a force field modification for Amber99sb is introduced and tested for the description of carboxyl group protonation. Our three states model is tested by titration simulations of Asp, Glu, and His, yielding a good agreement, reproducing the correct geometry of the groups in their different protonation forms. We further show that the ion concentration change due to the neutralizing “water” molecules does not significantly affect the protonation free energies of the titratable groups, suggesting that the three states model provides a good description of biomolecular dynamics at constant pH
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