caa a22 4500 445837004 CHVBK 20180317145333.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0714-5 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0714-5 Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves [Elektronische Daten] [K. Goodearl, S. Launois, T. Lenagan] The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action. In this paper, we prove that a family of quantum minors is the set of all quantum minors that belong to a given torus-invariant prime ideal of a quantum matrix algebra if and only if the corresponding family of minors defines a non-empty totally nonnegative cell in the space of totally nonnegative real matrices of the appropriate size. As a corollary, we obtain explicit generating sets of quantum minors for the torus-invariant prime ideals of quantum matrices in the case where the quantisation parameter q is transcendental over $${\mathbb{Q}}$$. The Author(s), 2010 Quantum matrices nationallicence Torus-invariant prime ideals nationallicence Quantum minors nationallicence Totally nonnegative cells nationallicence Symplectic leaves nationallicence Goodearl K. Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA aut Launois S. School of Mathematics, Statistics and Actuarial Science, University of Kent, CT2 7NF, Canterbury, Kent, UK aut Lenagan T. Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK aut Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 29-45 0025-5874 269:1-2<29 2011 269 209 https://doi.org/10.1007/s00209-010-0714-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0714-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goodearl K. Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA aut NATIONALLICENCE 700 1- Launois S. School of Mathematics, Statistics and Actuarial Science, University of Kent, CT2 7NF, Canterbury, Kent, UK aut NATIONALLICENCE 700 1- Lenagan T. Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 29-45 0025-5874 269:1-2<29 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer