{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835072,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] gave a new interpretation of what we called $\\ell$-partitions, also known as $(\\ell,0)$-Carter partitions. The primary interpretation of such a partition $\\lambda$ is that it corresponds to a Specht module $S^{\\lambda}$ which remains irreducible over the finite Hecke algebra $H_n(q)$ when $q$ is specialized to a primitive $\\ell^{th}$ root of unity. To accomplish this we relied heavily on the description of such a partition in terms of its hook lengths, a condition provided by James and Mathas. In this paper, I use a new description of the crystal $reg_\\ell$ which helps extend previous results to all $(\\ell,0)$-JM partitions (similar to $(\\ell,0)$-Carter partitions, but not necessarily $\\ell$-regular), by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers.<\/jats:p>","DOI":"10.37236\/391","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:10:14Z","timestamp":1578715814000},"source":"Crossref","is-referenced-by-count":0,"title":["Crystal Rules for $(\\ell,0)$-JM Partitions"],"prefix":"10.37236","volume":"17","author":[{"given":"Chris","family":"Berg","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,9,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r119\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r119\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:27:38Z","timestamp":1579303658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r119"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/391","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,9,1]]},"article-number":"R119"}}