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Representations of Lie superalgebras. (English) Zbl 1430.17029

Callegaro, Filippo (ed.) et al., Perspectives in Lie theory. Selected papers based on the presentations at the INdAM intensive research period, Pisa, Italy, December 2014 – February 2015. Cham: Springer. Springer INdAM Ser. 19, 125-177 (2017).
Summary: In these notes we give an introduction to representation theory of simple finite-dimensional Lie superalgebras. We concentrate on so called basic superalgebras. Those are superalgebras which have even reductive part and admit an invariant form. We start with structure theory of basic superalgebras emphasizing abstract properties of roots and then proceed to representations, trying to demonstrate the variety of methods: Harish-Chandra homomorphism, support variety, translation functors, Borel-Weil-Bott theory and localization.
For the entire collection see [Zbl 1387.17001].

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17B22 Root systems
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
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