JournalsprimsVol. 36 , No. 2DOI 10.2977/prims/1195143104

The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group

  • Thomas H. Lenagan

    University of Edinburgh, United Kingdom
  • Kenneth R. Goodearl

    University of California, Santa Barbara, USA
  • Laurent Rigal

    Université Jean-Monnet, Saint-Etienne, France
The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group cover

Abstract

We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum groups Oq(GLt(K)) and Oq(SLt(K)) on the quantized algebra Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)). (Here K is an arbitrary field and q an arbitrary nonzero scalar.) In both cases, the set of co-invariants is a subalgebra of Oq(Mm,t(K)) ⊗ Oq(Mt, n(K)), which we identify.