{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T06:41:17Z","timestamp":1772606477262,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For irreducible characters\u00a0$\\{ \\chi_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$,\u00a0induced sign characters\u00a0$\\{ \\epsilon_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$,\u00a0and induced trivial characters\u00a0$\\{ \\eta_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$\u00a0of the Hecke algebra $H_n(q)$,\u00a0and Kazhdan-Lusztig basis elements\u00a0$C'_w(q)$ with $w$ avoiding the patterns 3412 and 4231,\u00a0we combinatorially interpret the polynomials\u00a0$\\smash{\\chi_q^\\lambda(q^{\\ell(w)\/2} C'_w(q))}$,\u00a0$\\smash{\\epsilon_q^\\lambda(q^{\\ell(w)\/2} C'_w(q))}$,\u00a0and\u00a0$\\smash{\\eta_q^\\lambda(q^{\\ell(w)\/2} C'_w(q))}$.\u00a0This gives a new algebraic interpretation of chromatic quasisymmetric functions of Shareshian and Wachs,\u00a0and a new combinatorial interpretation of special cases of results of Haiman.\u00a0We prove similar results\u00a0for other $H_n(q)$-traces,\u00a0and confirm\u00a0a formula conjectured by Haiman.<\/jats:p>","DOI":"10.37236\/5021","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:27:02Z","timestamp":1578691622000},"source":"Crossref","is-referenced-by-count":13,"title":["Evaluations of Hecke Algebra Traces at Kazhdan-Lusztig Basis Elements"],"prefix":"10.37236","volume":"23","author":[{"given":"Samuel","family":"Clearman","sequence":"first","affiliation":[]},{"given":"Matthew","family":"Hyatt","sequence":"additional","affiliation":[]},{"given":"Brittany","family":"Shelton","sequence":"additional","affiliation":[]},{"given":"Mark","family":"Skandera","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,4,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:23Z","timestamp":1579239023000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5021","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,15]]},"article-number":"P2.7"}}