The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra $${\mathfrak{osp}(1|2n)}$$

2008 ◽  
Vol 281 (3) ◽  
pp. 805-826 ◽  
Author(s):  
S. Lievens ◽  
N. I. Stoilov ◽  
J. Van der Jeugt
Keyword(s):  
Fock Space ◽  
Lie Superalgebra ◽  
Irreducible Representations

scholarly journals PARAFERMIONS, PARABOSONS AND REPRESENTATIONS OF 𝔰𝔬(∞) AND 𝔬𝔰𝔭(1|∞)

2009 ◽  
Vol 20 (06) ◽  
pp. 693-715 ◽  
Author(s):  
N. I. STOILOVA ◽  
J. VAN DER JEUGT
Keyword(s):  
Lie Algebra ◽  
Fock Space ◽  
Complete Solution ◽  
Lie Superalgebra ◽  
Explicit Construction ◽  
Fock Spaces ◽  
Infinite Rank ◽  
Infinite Set ◽  
Basis Vectors

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(∞) and of the Lie superalgebra 𝔬𝔰𝔭(1|∞). 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.

scholarly journals GENERIC IRREDUCIBLE REPRESENTATIONS OF FINITE-DIMENSIONAL LIE SUPERALGEBRAS

1994 ◽  
Vol 05 (03) ◽  
pp. 389-419 ◽  
Author(s):  
IVAN PENKOV ◽  
VERA SERGANOVA
Keyword(s):  
Irreducible Module ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
Necessary And Sufficient

A theory of highest weight modules over an arbitrary finite-dimensional Lie superalgebra is constructed. A necessary and sufficient condition for the finite-dimensionality of such modules is proved. Generic finite-dimensional irreducible representations are defined and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic finite-dimensional irreducible module over any finite-dimensional Lie superalgebra. The conjecture is proved for several classes of Lie superalgebras, in particular for all solvable ones, for all simple ones, and for certain semi-simple ones.

scholarly journals Polynomial identities for simple Lie superalgebras

1987 ◽  
Vol 28 (3) ◽  
pp. 310-327 ◽  
Author(s):  
M. D. Gould
Keyword(s):  
Tensor Product ◽  
Lie Superalgebra ◽  
Weight Vector ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Polynomial Identities ◽  
Minimal Weight ◽  
Finite Dimensional ◽  
Basic Classical Lie Superalgebra

AbstractPolynomial identities for the generators of a simple basic classical Lie superalgebra are derived in arbitrary representations generated by a maximal (or minimal) weight vector. The infinitesimal characters occurring in the tensor product of two finite dimensional irreducible representations are also determined.

BRST AND l(1, 1)

1993 ◽  
Vol 05 (01) ◽  
pp. 191-208 ◽  
Author(s):  
S. S. HORUZHY ◽  
A. V. VORONIN
Keyword(s):  
Brst Symmetry ◽  
Lie Superalgebra ◽  
Irreducible Representations ◽  
Close Connection ◽  
Infinite Dimensional ◽  
Brst Charge ◽  
New Formula

A very close connection between the BRST symmetry and the Lie superalgebra l(1, 1) is pointed out and studied. Structure of l(1, 1), its involutions and automorphisms are described. Absence of infinite-dimensional irreducible representations (IR) of l(1, 1) is proved. The rigorous construction and decomposition into IR is performed for the class of l(1, 1) representations corresponding to physical BRST theories and consisting of infinite-dimensional doubly involutive representations in J-spaces. As a first output of the l(1, 1) formalism, a new formula for the BRST charge is derived.

scholarly journals Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

2014 ◽  
Vol 55 (1) ◽  
pp. 011703 ◽  
Author(s):  
Mark D. Gould ◽  
Phillip S. Isaac ◽  
Jason L. Werry
Keyword(s):  
Lie Superalgebra ◽  
Irreducible Representations ◽  
Matrix Elements

scholarly journals Highest weight irreducible representations of the Lie superalgebra gl(1|∞)

1999 ◽  
Vol 40 (3) ◽  
pp. 1574-1594 ◽  
Author(s):  
T. D. Palev ◽  
N. I. Stoilova
Keyword(s):  
Lie Superalgebra ◽  
Irreducible Representations ◽  
Highest Weight
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