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arXiv · 1509.03869

The representation theory of noncommutative $\mathcal{O}(\text{GL}_2)$

Theo Raedschelders·Michel Van den Bergh
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Abstract

In our companion paper "The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary" we used the Tannaka-Krein formalism to study the universal coacting Hopf algebra aut(A) for a Koszul Artin-Schelter regular algebra A. In this paper we study in detail the case A=k[x,y]. In particular we give a more precise description of the standard and costandard representations of aut(A) as a coalgebra and we show that the latter can be obtained by induction from a Borel quotient algebra. Finally we give a combinatorial characterization of the simple aut(A)-representations as tensor products of end(A)-representations and their duals.

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BibTeXRIS

Theo Raedschelders, Michel Van den Bergh. 2015-09-13. The representation theory of noncommutative $\mathcal{O}(\text{GL}_2)$. https://arxiv.org/abs/1509.03869

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