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arXiv · 1604.00338

On universal quadratic identities for minors of quantum matrices

Vladimir Danilov·Alexander Karzanov
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Abstract

We give a complete combinatorial characterization of homogeneous quadratic relations of "universal character" valid for minors of quantum matrices (more precisely, for minors in the quantized coordinate ring $O_q(M_{m,n}(K))$ of $m\times n$ matrices over a field $K$, where $q\in K^\ast$). This is obtained as a consequence of a study of quantized minors of matrices generated by paths in certain planar graphs, called SE-graphs, generalizing the ones associated with Cauchon diagrams. Our efficient method of verifying universal quadratic identities for minors of quantum matrices is illustrated with many appealing examples.

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Vladimir Danilov, Alexander Karzanov. 2016-04-01. On universal quadratic identities for minors of quantum matrices. https://arxiv.org/abs/1604.00338

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