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Sergeev, Alexander N.; Veselov, Alexander P.

Grothendieck rings of basic classical Lie superalgebras. (English) Zbl 1278.17006

Ann. Math. (2) 173, No. 2, 663-703 (2011).
Summary: The Grothendieck rings of finite dimensional representations of the basic classical Lie superalgebras are explicitly described in terms of the corresponding generalized root systems. We show that they can be interpreted as the subrings in the weight group rings invariant under the action of certain groupoids called super Weyl groupoids.

Cited in 17 Documents

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
18F30 Grothendieck groups (category-theoretic aspects)
19A49 \(K_0\) of other rings

Keywords:

Grothendieck ring; Lie superalgebras; representations
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References:

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