<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Evangelou</style></author><author><style face="normal" font="default" size="100%">M. Maliakas</style></author><author><style face="normal" font="default" size="100%">D.-D. Stergiopoulou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On stability and nonvanishing of homomorphism spaces between Weyl modules</style></title><secondary-title><style face="normal" font="default" size="100%">Algebraic Combinatorics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://alco.centre-mersenne.org/articles/10.5802/alco.397/</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">7</style></volume><pages><style face="normal" font="default" size="100%">1761-1792</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Consider the general linear group $G=GL_{n}(K)$ defined over an infinite field $K$ of positive characteristic $p$. We denote by $\Delta(\lambda)$ the Weyl module of $G$ which corresponds to a partition $\lambda$. Let $\lambda, \mu$ be partitions of $r$ and let $\gamma$ be partition with all parts divisible by $p$. In the first main result of this paper, we find sufficient conditions on $\lambda, \mu and \gamma$ so that $Hom_G(\Delta(\lambda),\Delta(\mu)) \simeq Hom_G(\Delta(\lambda +\gamma),\Delta(\mu +\gamma))$, thus providing an answer to a question of D. Hemmer. As corollaries we obtain stability and periodicity results for homomorphism spaces. In the second main result we find related sufficient conditions on $\lambda, \mu$ and $p$ so that $Hom_G(\Delta(\lambda),\Delta(\mu))$ is nonzero. An explicit map is provided that corresponds to the sum of all semistandard tableaux of shape $\mu$ and weight $\lambda$.</style></abstract></record></records></xml>