{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:00:36Z","timestamp":1760061636721},"reference-count":37,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,10,1]],"date-time":"2016-10-01T00:00:00Z","timestamp":1475280000000},"content-version":"unspecified","delay-in-days":274,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>Let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline4\" \/><jats:tex-math>$UY_{n}(q)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>be a Sylow<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline5\" \/><jats:tex-math>$p$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-subgroup of an untwisted Chevalley group<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline6\" \/><jats:tex-math>$Y_{n}(q)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>of rank<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline7\" \/><jats:tex-math>$n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>defined over\u00a0<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline8\" \/><jats:tex-math>$\\mathbb{F}_{q}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>where<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline9\" \/><jats:tex-math>$q$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is a power of a prime<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline10\" \/><jats:tex-math>$p$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We partition the set<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline11\" \/><jats:tex-math>$\\text{Irr}(UY_{n}(q))$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>of irreducible characters of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline12\" \/><jats:tex-math>$UY_{n}(q)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>into families indexed by antichains of positive roots of the root system of type<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline13\" \/><jats:tex-math>$Y_{n}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We focus our attention on the families of characters of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline14\" \/><jats:tex-math>$UY_{n}(q)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>which are indexed by antichains of length<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline15\" \/><jats:tex-math>$1$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Then for each positive root<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline16\" \/><jats:tex-math>$\\unicode[STIX]{x1D6FC}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>we establish a one-to-one correspondence between the minimal degree members of the family indexed by<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline17\" \/><jats:tex-math>$\\unicode[STIX]{x1D6FC}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and the linear characters of a certain subquotient<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline18\" \/><jats:tex-math>$\\overline{T}_{\\unicode[STIX]{x1D6FC}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline19\" \/><jats:tex-math>$UY_{n}(q)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. For<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline20\" \/><jats:tex-math>$Y_{n}=A_{n}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>our single root character construction recovers, among other things, the elementary supercharacters of these groups. Most importantly, though, this paper lays the groundwork for our classification of the elements of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline21\" \/><jats:tex-math>$\\text{Irr}(UE_{i}(q))$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline22\" \/><jats:tex-math>$6\\leqslant i\\leqslant 8$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000401_inline23\" \/><jats:tex-math>$\\text{Irr}(UF_{4}(q))$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1112\/s1461157016000401","type":"journal-article","created":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T07:12:21Z","timestamp":1476688341000},"page":"303-359","source":"Crossref","is-referenced-by-count":7,"title":["On the characters of the Sylow -subgroups of untwisted Chevalley groups"],"prefix":"10.1112","volume":"19","author":[{"given":"Frank","family":"Himstedt","sequence":"first","affiliation":[]},{"given":"Tung","family":"Le","sequence":"additional","affiliation":[]},{"given":"Kay","family":"Magaard","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2016,10,1]]},"reference":[{"key":"S1461157016000401_r8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(85)90026-X"},{"key":"S1461157016000401_r35","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2005-043-4"},{"key":"S1461157016000401_r11","unstructured":"11. 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