Highest weight irreducible representations of the Lie superalgebra gl(1

@article{Palev1998HighestWI,
  title={Highest weight irreducible representations of the Lie superalgebra gl(1},
  author={Tchavdar D. Palev and N I Stoilova},
  journal={Journal of Mathematical Physics},
  year={1998},
  volume={40},
  pages={1574-1594}
}
Two classes of irreducible highest weight modules of the general linear Lie superalgebra gl(1|∞) 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. 

References

SHOWING 1-10 OF 36 REFERENCES

Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(

Two classes of irreducible highest weight modules of the general linear Lie algebra gl(∞), corresponding to two different Borel subalgebras, are constructed. Both classes contain all unitary

Irreducible finite‐dimensional representations of the Lie superalgebra gl(n/1) in a Gel’fand–Zetlin basis

All finite‐dimensional irreducible representations of the general linear Lie superalgebra gl(n/1) are studied. For each representation, a concept of a Gel’fand–Zetlin basis is defined. Expressions

Canonical realizations of Lie superalgebras: Ladder representations of the Lie superalgebra A(m,n)

A simple formula for realizations of Lie superalgebras in terms of Bose and Fermi creation and annihilation operators is given. The essential new feature is that Bose and Fermi operators mutually

Fock space representations of the Lie superalgebra A(0,n)

An infinite class of finite‐dimensional irreducible representations and one particular infinite‐dimensional representation of the special linear superalgebra of an arbitrary rank is constructed. For

AUTOMORPHISMS OF SIMPLE LIE SUPERALGEBRAS

This paper gives an enumeration of the outer automorphisms of simple finite-dimensional complex Lie superalgebras, the nonisomorphic infinite-dimensional Lie superalgebras associated with these

Dimension formulas for the Lie superalgebra sl(m/n)

Although character formulas for simple finite‐dimensional modules of the Lie superalgebra sl(m/n) are not known in general, they are known in the cases of so‐called typical and of singly atypical

Quantum deformation of Bose parastatistics

A q‐deformation of the transformation of the Chevalley basis to an odd basis of generators of the universal enveloping of the Lie superalgebra G(n)≡osp(1‖2n) is presented. It is shown that one thus

A Lie superalgebraic interpretation of the para‐Bose statistics

We show that n pairs of para‐Bose operators generate the classical simple orthosymplectic Lie superalgebra osp(1,2n) ≡B (0,n). The creation and annihilation operators are negative and positive root

Lie-superalgebraical approach to the second quantization

The Lie superalgebraical properties of the ordinary quantum statistics are discussed. It is indicated that the algebra generated byn pairs of Fermi operator is isomorphic to the classical simple Lie