## Irreducible representations of solvable Lie superalgebras

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- by Alexander Sergeev PDF
- Represent. Theory
**3**(1999), 435-443 Request permission

## Abstract:

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V. Kac is refined. In reality these representations are not just induced from a polarization but are twisted ones, as infinite dimensional representations of solvable Lie algebras. Various cases of irreducibility (general and of type Q) are classified.## References

- J. N. Bernstein and D. A. Leĭtes,
*The superalgebra $Q(n)$, the odd trace and the odd determinant*, C. R. Acad. Bulgare Sci.**35**(1982), no. 3, 285–286. MR**677839** - Jacques Dixmier,
*Enveloping algebras*, Graduate Studies in Mathematics, vol. 11, American Mathematical Society, Providence, RI, 1996. Revised reprint of the 1977 translation. MR**1393197**, DOI 10.1090/gsm/011 - V. G. Kac,
*Lie superalgebras*, Advances in Math.**26**(1977), no. 1, 8–96. MR**486011**, DOI 10.1016/0001-8708(77)90017-2 - Leites D. (ed.),
*Seminar on supermanifolds*#22, Reports of the Department of Mathematics of Stockholm University, 1988-4, 1–12. - I. M. Shchepochkina,
*Maximal solvable subalgebras of the Lie superalgebras $\textrm {gl}(m|n)$ and $\textrm {sl}(m|n)$*, Funktsional. Anal. i Prilozhen.**28**(1994), no. 2, 92–94 (Russian); English transl., Funct. Anal. Appl.**28**(1994), no. 2, 147–149. MR**1283268**, DOI 10.1007/BF01076514

## Additional Information

**Alexander Sergeev**- Affiliation: On leave of absence from Balakovo Institute of Technique of Technology and Control, Branch of Saratov State Technical University, Russia; Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden
- Email: mleites@matematik.su.se (subject: for Sergeev)
- Received by editor(s): November 4, 1998
- Received by editor(s) in revised form: September 8, 1999
- Published electronically: November 9, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Represent. Theory
**3**(1999), 435-443 - MSC (1991): Primary 17A70; Secondary 17B30
- DOI: https://doi.org/10.1090/S1088-4165-99-00086-2
- MathSciNet review: 1722111