Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
Type of Publication:  Journal article 
Publication status:  Published 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:35221r2z1qecqw47p1 
Author:  Kobert, Tim; Scheiderer, Claus 
Year of publication:  2022 
Published in:  manuscripta mathematica ; 169 (2022), 12.  pp. 185208.  Springer.  ISSN 00252611.  eISSN 14321785 
DOI (citable link):  https://dx.doi.org/10.1007/s0022902101337z 
Summary: 
Let K be a compact Lie group and V a finitedimensional representation of K. The orbitope of a vector x∈V is the convex hull Ox of the orbit Kx in V. We show that if V is polar then Ox is a spectrahedron, and we produce an explicit linear matrix inequality representation. We also consider the coorbitope Oox, which is the convex set polar to Ox. We prove that Oox is the convex hull of finitely many Korbits, and we identify the cases in which Oox is itself an orbitope. In these cases one has Oox=c⋅Ox with c>0. Moreover we show that if x has “rational coefficients” then Oox is again a spectrahedron. This provides many new families of doubly spectrahedral orbitopes. All polar orbitopes that are derived from classical semisimple Lie algebras can be described in terms of conditions on singular values and Ky Fan matrix norms.

Subject (DDC):  510 Mathematics 
Link to License:  In Copyright 
Bibliography of Konstanz:  Yes 
Refereed:  Yes 
KOBERT, Tim, Claus SCHEIDERER, 2022. Spectrahedral representation of polar orbitopes. In: manuscripta mathematica. Springer. 169(12), pp. 185208. ISSN 00252611. eISSN 14321785. Available under: doi: 10.1007/s0022902101337z
@article{Kobert2022Spect54765, title={Spectrahedral representation of polar orbitopes}, year={2022}, doi={10.1007/s0022902101337z}, number={12}, volume={169}, issn={00252611}, journal={manuscripta mathematica}, pages={185208}, author={Kobert, Tim and Scheiderer, Claus} }
Kobert_21r2z1qecqw47p1.pdf  22 