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.
Funding
This work has been partially supported by the EPSRC (grant EP/E004008/1), European Union through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652) and ESF programme MISGAM.
History
School
Science
Department
Mathematical Sciences
Published in
ANNALS OF MATHEMATICS
Volume
173
Issue
2
Pages
663 - 703 (41)
Citation
SERGEEV, A.N. and VESELOV, A.P., 2011. Grothendieck rings of basic classical Lie superalgebras. Annals of Mathematics, 173 (2), pp. 663-703.