Grothendieck rings of basic classical Lie superalgebras

Abstract

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.

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Authors

Alexander N. Sergeev

Loughborough University
Loughborough, UK

and

Saratov State University
Saratov
Russia

Alexander P. Veselov

Loughborough University
Loughborough, UK
and

Moscow State University
Moscow
Russia