Generic Irreducible Representations of Finite-Dimensional Lie Superalgebras

@inproceedings{Penkov1994GenericIR,
  title={Generic Irreducible Representations of Finite-Dimensional Lie Superalgebras},
  author={Ivan Penkov and Vera Serganova},
  year={1994}
}
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… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 24 REFERENCES

Differentiably simple Lie superalgebras and some representation theory, Ph.D

  • S.-J. Cheng
  • 1992

Kazhdan-Lusztig polynomials for the Lie superalgebras GL(m/n), Yale Univ

  • V. Serganova
  • 1992

On the composition factors of Kac modules for the Lie superalgebras sl(m/n)

  • J. Van der Jeugt, J.W.B. Hughes, R. C. King
  • J. Math. Phys
  • 1992

Scheunert , The theory of Lie superalgebras , Lect

  • M.
  • 1992

Invariant differential operators and irreducible finite-dimensional representations of the Hamiltonian and Poisson Lie superalgebras

  • A. Shapovalov
  • Serdica (in Russian)
  • 1987