{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841099,"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>Coloured generalised Young diagrams $T(w)$ are introduced that are in bijective correspondence with the elements $w$ of the Weyl-Coxeter group $W$ of $\\mathfrak{g}$, where $\\mathfrak{g}$ is any one of the classical affine Lie algebras $\\mathfrak{g}=A^{(1)}_\\ell$, $B^{(1)}_\\ell$, $C^{(1)}_\\ell$, $D^{(1)}_\\ell$, $A^{(2)}_{2\\ell}$, $A^{(2)}_{2\\ell-1}$ or $D^{(2)}_{\\ell+1}$.  These diagrams are coloured by means of periodic coloured grids, one for each $\\mathfrak{g}$, which enable $T(w)$ to be constructed from any expression $w=s_{i_1}s_{i_2}\\cdots s_{i_t}$ in terms of generators $s_k$ of $W$, and any (reduced) expression for $w$ to be obtained from $T(w)$.  The diagram $T(w)$ is especially useful because $w(\\Lambda)-\\Lambda$ may be readily obtained from $T(w)$ for all $\\Lambda$ in the weight space of $\\mathfrak{g}$. With $\\overline{\\mathfrak{g}}$ a certain maximal finite dimensional simple Lie subalgebra of $\\mathfrak{g}$, we examine the set $W_s$ of minimal right coset representatives of $\\overline{W}$ in $W$, where $\\overline{W}$ is the Weyl-Coxeter group of $\\overline{\\mathfrak{g}}$.  For $w\\in W_s$, we show that $T(w)$ has the shape of a partition (or a slight variation thereof) whose $r$-core takes a particularly simple form, where $r$ or $r\/2$ is the dual Coxeter number of $\\mathfrak{g}$.  Indeed, it is shown that $W_s$ is in bijection with such partitions.<\/jats:p>","DOI":"10.37236\/931","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:52:14Z","timestamp":1578700334000},"source":"Crossref","is-referenced-by-count":0,"title":["Coloured Generalised Young Diagrams for Affine Weyl-Coxeter Groups"],"prefix":"10.37236","volume":"14","author":[{"given":"R. C.","family":"King","sequence":"first","affiliation":[]},{"given":"T. A.","family":"Welsh","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:04:53Z","timestamp":1579302293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/931","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,17]]},"article-number":"R13"}}