Fusion Rings for Quantum Groups

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  • Henning Haahr Andersen, Denmark
  • Catharina Stroppel, University of Bonn
We study the fusion rings of tilting modules for a quantum group at a root of
unity modulo the tensor ideal of negligible tilting modules. We identify them in type A
with the combinatorial rings from Korff, C., Stroppel, C.: The sl(ˆn)k-WZNW fusion ring:
a combinato-rial construction and a realisation as quotient of quantum cohomology. Adv.
Math. 225(1), 200–268, (2010) and give a similar description of the sp2n-fusion ring in
terms of non-commutative symmetric functions. Moreover we give a presentation of all
fusion rings in classical types as quotients of polynomial rings. Finally we also compute the
fusion rings for type G2.
Original languageEnglish
JournalAlgebras and Representation Theory
Volume17
Issue6
Pages (from-to)1869-1888
Number of pages20
ISSN1386-923X
Publication statusPublished - 29 May 2014

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