152 research outputs found
Highest weight irreducible representations of the Lie superalgebra
Two classes of irreducible highest weight modules of the general linear Lie
superalgebra are constructed. Within each module a basis is
introduced and the transformation relations of the basis under the action of
the algebra generators are written down.Comment: 24 pages, TeX; Journ. Math. Phys. (to be published
Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)
The goal of this paper is to give an explicit construction of the Fock spaces
of the parafermion and the paraboson algebra, for an infinite set of
generators. This is equivalent to constructing certain unitary irreducible
lowest weight representations of the (infinite rank) Lie algebra so(\infty) and
of the Lie superalgebra osp(1|\infty). A complete solution to the problem is
presented, in which the Fock spaces have basis vectors labelled by certain
infinite but stable Gelfand-Zetlin patterns, and the transformation of the
basis is given explicitly. We also present expressions for the character of the
Fock space representations
Highest weight representations of the quantum algebra U_h(gl_\infty)
A class of highest weight irreducible representations of the quantum algebra
U_h(gl_\infty) is constructed. Within each module a basis is introduced and the
transformation relations of the basis under the action of the Chevalley
generators are explicitly written.Comment: 7 pages, PlainTe
Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor
representations of the Lie superalgebra gl(m|n). Explicit expressions for the
generators of the Lie superalgebra acting on this basis are determined.
Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of
any covariant tensor representation of gl(m|n) with the natural representation
V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed.
Both results are steps for the explicit construction of the parastatistics Fock
space.Comment: 16 page
Jacobson generators of the quantum superalgebra and Fock representations
As an alternative to Chevalley generators, we introduce Jacobson generators
for the quantum superalgebra . The expressions of all
Cartan-Weyl elements of in terms of these Jacobson generators
become very simple. We determine and prove certain triple relations between the
Jacobson generators, necessary for a complete set of supercommutation relations
between the Cartan-Weyl elements. Fock representations are defined, and a
substantial part of this paper is devoted to the computation of the action of
Jacobson generators on basis vectors of these Fock spaces. It is also
determined when these Fock representations are unitary. Finally, Dyson and
Holstein-Primakoff realizations are given, not only for the Jacobson
generators, but for all Cartan-Weyl elements of .Comment: 27 pages, LaTeX; to be published in J. Math. Phy
Wigner quantum oscillators. Osp(3/2) oscillators
The properties of the three-dimensional noncanonical osp(3/2) oscillators,
introduced in J.Phys. A: Math. Gen. {\bf 27} (1994) 977, are further studied.
The angular momentum M of the oscillators can take at most three values
M=p-1,p,p+1, which are either all integers or all half-integers. The
coordinates anticommute with each other. Depending on the state space the
energy spectrum can coincide or can be essentially different from those of the
canonical oscillator. The ground state is in general degenerated.Comment: TeX, Preprint INRNE-TH-94/3, 17
2-DE proteomics analysis of drought treated seedlings of Quercus ilex supports a root active strategy for metabolic adaptation in response to water shortage
Holm oak is a dominant tree in the western Mediterranean region. Despite being well adapted to dry hot climate, drought is the main cause of mortality post-transplanting in reforestation programs. An active response to drought is critical for tree establishment and survival. Applying a gel-based proteomic approach, dynamic changes in root proteins of drought treated Quercus ilex subsp. Ballota [Desf.] Samp. seedlings were followed. Water stress was applied on 20 day-old holm oak plantlets by water limitation for a period of 10 and 20 days, each followed by 10 days of recovery. Stress was monitored by changes in water status, plant growth, and electrolyte leakage. Contrary to leaves, holm oak roots responded readily to water shortage at physiological level by growth inhibition, changes in water status and membrane stability. Root proteins were extracted using trichloroacetate/acetone/phenol protocol and separated by two-dimensional electrophoresis. Coomassie colloidal stained gel images were analyzed and spot intensity data subjected to multivariate statistical analysis. Selected consistent spots in three biological replicas, presenting significant changes under stress, were subjected to MALDI-TOF mass spectrometry (peptide mass fingerprinting and MS/MS). For protein identification, combined search was performed with MASCOT search engine over NCBInr Viridiplantae and Uniprot databases. Data are available via ProteomeXchange with identifier PXD002484. Identified proteins were classified into functional groups: metabolism, protein biosynthesis and proteolysis, defense against biotic stress, cellular protection against abiotic stress, intracellular transport. Several enzymes of the carbohydrate metabolism decreased in abundance in roots under drought stress while some related to ATP synthesis and secondary metabolism increased. Results point at active metabolic adjustment and mobilization of the defense system in roots to actively counteract drought stress
Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics
Fock space representations of the Lie superalgebra and of its
quantum analogue are written down. The results are based on a
description of these superalgebras via creation and annihilation operators. The
properties of the underlying statistics are shortly discussed.Comment: 12 pages, PlainTex; to appear in J. Phys. A: Math. Ge
Microscopic and macroscopic properties of A-superstatistics
The microscopic and the macroscopic properties of A-superstatistics, related
to the class A(0,n-1)\equiv sl(1|n) of simple Lie superalgebras are
investigated. The algebra sl(1|n) is described in terms of generators f_1^\pm,
>..., f_n^\pm, which satisfy certain triple relations and are called Jacobson
generators. The Fock spaces of A-superstatistics are investigated and the Pauli
principle of the corresponding statistics is formulated. Some thermal
properties of A-superstatistics are constructed under the assumption that the
particles interact only via statistical interaction imposed by the Pauli
principle. The grand partition function and the average number of particles are
written down explicitly in the general case and in two particular examples: 1)
the particles have one and the same energy and chemical potential; 2) the
energy spectrum of the orbitals is equidistant.Comment: 26 pages, 3 figure
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