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Ties for the integral group ring of the symmetric group

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(1)Ties for the integral group ring of the symmetric group Matthias Kuenzer. To cite this version: Matthias Kuenzer. Ties for the integral group ring of the symmetric group. Mathematics [math]. Universität Ulm, 1998. English. �tel-00001202�. HAL Id: tel-00001202 https://tel.archives-ouvertes.fr/tel-00001202 Submitted on 8 Mar 2002. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(78) hSrYdngvibld*uidn˜Ph }l‚ ›wzy3uis|jek|hC˜š™0^ëacbldng’dùs`uy Ô à ©£s|}­r3yYg’s¾yY}­v$jls|k`s|}ldnyYg¤¹h gimñ‚edPÄz}ldP‚%h }Ls`viup˜Ph k|weÊ m} ú ÊÊ ûz¿ƒ s`rYdn}Lj­¢Ÿvxbld9€qgiyYmm¨y3vigis” Ê ú áà ù àØ ûl¿ ¢As`dnk`‚ls|}lƒvxbed¨s|}e˜nk|weuis|hY}Ÿh3¤vxbld9§Af0dn˜šÊ b­v

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(80) vxbed$h3vxbldPg¡˜Ph k|wemT} ú à ûl¿l¦¬bldPgidp†

(81) u’všy3}l‚lu¬¤¹h g$Û¶†­Ü¿erCs¾y Ê ù Ê ú Ê û ú à û Ì l l ÛØ Ü ú ítû í l Ûà Ø P ú à û Üu yYu?˜ªy3}Šj0d‚ldPgistr dn‚ŠdY^ƒl^{¤¹gih mœgidPu’vxg’s|˜vxs|hY}

(82) hY¤zvxbldcmyYf

(83) ƒ str dP}

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(85) †e^ ¡uis`}lƒ—vxbls`u?s|u’h mŠh giflbes|uim‘¤¹hYg?s|u’h mhYgiflbls`˜u’wljlu’vis`viwevxs`h }¿Y¦+dcuidPd¬vibzy3v vxblà d s|}l˜Pk|wlÊ u’s|h }h3¤evxbed§Cf7dP˜šb›vk¾y3v’vxs`˜nd&s|}­vih¡stvxu"‚lwzy3k­s|u"s|u’h mhYgiflbls`˜¬Û¶y3uy¬‚ls¾y3ƒ gxyYm¨Ü½vih¡vibld s|}l˜Pk|wlu’s|h } ú à û ç ú à û ^?acb›wluyY}

(86) dPk|dnmŠdn}­v&h3¤zvxbldu’dn˜Ph }l‚ŠÂCwlyYuis`jlk|hC˜š™qgidnmyYs`}lus`}›vidnƒ giyYkej­¢pk|d¤«v&˜nh } ’wlƒ­y3vis|h } ¦¬s`vxb ú àí í û ¿l¦¬bls|˜šb*mdnyY}luvibzy3v ØØ s`uc‚ls`rCs`uis|jek|d—j­¢*†e^ –K—P˜š™d›œžkŸ ˜¢¡. <;. 8$. ( ". =( ". ( " >(. *) +  )  )  ). #. ( ". #( ". ?( . . /@. 

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(91) fzy3vibùy3k|ƒ dPjlgxy

(92) mŠhA‚lwek|h

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(96) fzy{vxb‰yYk|ƒ dPjlgxy

(97) mŠhA‚ewlk|h

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(100) hY¤¬uiwe˜šb yù›wzy3uis|jek|hC˜š™0^ ¼½weg’vxbedngimŠh g’dY¿?st¤¬s|}Lu’wl˜šbøyY}Ldn}e‚lh mŠh gÁ© flbls|u’mâgis`}lƒl¿zdPm„j7dP‚l‚ldP‚ùs|}­vihy uis`}lƒ k`dm¨y3vigis” #gis`}lƒl¿ldPs`vibldngcvxbed$f0h u’s`vxs`h } ¨hYg¡stvxuvigxyY}lu’f7hYuid ˜ªyYg’gis|dPuqy#uis|}eƒ k|d ÁA©5vxs`d„¤¹h g—dnyY˜šb £ z¿"s`viugxyY‚ls`˜ªyYk¥s|uƒ str dP}Ij­¢s`mf0h uis`}lƒ9u’s|}lƒ k`d Áe©ßvxs|dPuh }vxbld m¨yYs`}#‚ls¾y3ƒ h }zyYk7dn}­vxg’s|dPuÛ[Žc^`_ ^‡† ]­Ü^ ¼½hYgs|}luÁvšyY}e˜ndY¿z˜Ph }lu’s|‚ldPgvxbld„Ó à ©£h g’‚ldng®Ó à Ô à ¿ls|u’h mhYgiflbls`˜žvihŠstvxus`m¨y3ƒ d æ wl}e‚ldngcvxbed$dPm„j0dn‚A© ‚ls|}lƒ ƒ str dP}*s`}IÛߧ]e^~YÜ^&ð5vxu¬giyY‚ls|˜nyYks`ucƒ s`rYdn}*j›¢ à Ê æT£ † ú àÊà û ù† ¦¬bldng’d†

(101) u’vxyY}l‚lu¬¤¹h g$Û[†­Ü^ žuis`}lƒ

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(103) Û¹˜P¤ú^7yYk|u’hù_ ^t_ ^Œ›Ü^ ¤ dp¦¬s`k|k"}lhYv®flwlgiu’wldvibls|u f7h u’uis`jls|k`s`v£¢ ¿CblhS¦+dPr dPgn^ ž}lstvxu„y3gid#y flg’h mŠs|}ldP}›vd eyYmŠflk|dŠ¤¹h gvibld9wluiyYƒ d9hY¤¬my3vigist Im„wek`vxs`flk|s`˜ªy3vis|h }¯^#ð£}øƒYdn}ldPgxyYk¶¿vxbld vxs|d ¤¹h g’myYk|k`h1¦¬uqvxh*vxbls`}l™hY¤c˜nyYk|˜Pwlk¾y{vxs|hY}luqs|}Ivibld¨ƒYgih wlfIgis`}lƒ yYuphY¤c˜nyYk|˜Pwlk¾y3vis|h }eus|}Ïmy3vigis|˜Pdnu uiwlj ’dP˜Pvvih9uih mŠdpvis|dPun^¼zh gžs|}luÁvšyY}l˜PdY¿0vxbld„˜Pdn}­vxdPgn¿hYgyYk|u’h9y¨my{ As|myYkV˜Ph mmwevšy3vis`rYduiwej7h g’‚ldng Û¶y„vxh g’wlušÜj0dn˜Ph md—rCs`uis|jek|dY^ acbld—‚ldP˜nh mŠf7hYuis`vis|h }m¨y{vxgis” Šm¨yª¢j7dž˜ªyYk`˜nwlk|y3vxdP‚9p j­¢9˜Ph wl}­vxs`}lƒ„m„wlktvxs`flk|s`˜ns`vis|dPu?hY¤"uis`mfek|d¡k¾y3v’vxs|˜Pdnu s|}Lflg’h ’dn˜vxstr ds|}l‚edn˜nhYmf0h uxy3jlk|dk¾y3v’vxs|˜PdnuP^ ô"dv ‚edn}lhYvid9vxbld*§Cf7dP˜šb›vŠk|y3vivis|˜ndhSr dnƒ g¨Ó ¦ NÔ g vxh vxbldfzyYg’vis`vis|h } xLhY ¤ z¥d¿ ÁLflg’s|mŠdY^ôVdPv j0d9Vy Áe©£g’dnƒ wek¾yYgqfzyYgÁvxstvxs|hY}¿"k|dPv £ j7dŠvxbld ˜nh g’gidnu’f7hY}l‚ls|}eƒ uis`mflk`dmŠhC‚lwlk|d3¿k`dPv ‚ldn}ehYvxd9stvxupflgih ’dP˜Pvis`r d¨˜nhSr dPg

(104) h1rYdngÓ ¦ NÔ ge^Éh }luis`‚ldng vxbldquidPms`uis`mflk`d—ôVhCdP¦c¢#k|yS¢Ydng’u p p p p ƒ ¯ ý £JÛ WÁ Ü Û 3Á Ü ¿ ¤ dqh jevxyYs|}9vibldq‚lp dn˜Ph mŠf7h u’s`vis|h }#}›wlm„j0dng ý _j £ h í ‚ls|m "í¡h m ßÅ Æ Û u߯ «Ü £ í¡h 7m Ê Å Æ Û p ƒ u߯ p ¹Ü í ‚ls|m £ ‚ls`m VížhYm Ê ÅtÆAÛ u p Á ƒ Ü p £ ‚ls`m úxížhYm Ê ÅtÆAÛ u p Ü ƒ í¡h 7m Ê ÅtÆAÛ u Á p @Ü û £ ‚ls`m ú ížhYm Ê ÅtÆAÛ u p Ü ÁžížhYVm Ê ÅtÆAÛ u Ü û £ g’®™ Ê [ížh 7m Ê Å9ÆeÛ u Ü p £ ‚ls`7m Äí¡h 7m ÄNÅ9Æl‹Û S uS Ü ¿ #. .

(105).

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(107). 7.

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(109). s h . is. v. po. . 1j z m. r.  . 8r. . 7. Kr. . Kr. .  . #. h  . . #.

(110) A s|s`s ˆ‰p h ƒ gidPhSr p dngP¿zwluxy3ƒ d—hY¤VvibldgxyY‚es|˜ªy3k7dP}zyYjlk`dnuwlu+vxh

(111) gidÄz}ld®vibls|u˜ªyYk`˜nwlk|y3vxs`h }Švih„vxbld—ô"hCdP¦c¢k¾yª¢Ydngiuch3¤ Á ^ ¤ d¦¬gistvxd £Ó ¦ ÔNg ø ¿ ø j0dns|}eƒy

(112) flg’s|mŠs`vis`r džs|‚ldPmf0hYvidn}­v¬hY¤Ó ¦ ÔNgŠyY}l‚*h jevxyYs|} p p ížhYm ÅtÆAÛ u¯ ¾Ü £ ížhYmÊ ÅtÆeÛ u¯ ¾Ü p p ƒ £ ížhYmÊ p Å Æ Û p u ƒ WÁ p Ü ížh 7m p Ê Å Æ Û Ñu 3Á Ü £ WÁ Ü ø lÛ WÁ Ü ¿ ø lÛ ¼½hYà g®s|}eu’všy3}l˜nd3¿í s|}ùvibld„u’s`vxwly3vxs`h }ùhY¤žÛ¶§ ]e^~ ܬ¦+d

(113) h jevxyYs|}*¤¹h g z £È†e¿ Á3£J†AN¿ x3£âÛ¶~ uª_1Ü¿ £âÛ¶† Ü¿ £È_ ú íí û ] yY}e‚ ]£œ_ ø í¡h m Å Û à u߯ ’Ü £ ø à í Û Ê Ø ƒ ø† í Ø à Ü ƒ ø à Û Ø Ø ø† Ø Ü ú íí ûú à û ú íÑí ûú à û £ £ Ó ƒ ®† ¿ ®užy‚ls`uxyY‚er3yY}­vxyYƒ d¦dpmdP}­vxs|hY}*vibzy3v¬vxbld$uiwejlƒ gihYwlflu—y3gid$bls|‚l‚edn}^c¼zh g¬s`}lu’vxyY}l˜nd3¿zvxhŠ˜ªyYk`˜nwlk|y3vxd r dngÁvxs`˜ndnuhY¤cs|}e‚ldn˜Ph mf0h uiyYjlk|d k|y3vivis|˜ndPuqh1rYdngÓ ¦ NÔ geJ¿ Á flg’s|mŠdY¿h }ldŠuidndPmupvxhùj0d ¤¹h gi˜Pdn‚Ïvihùwlu’d vxbldŠgidPflgidPuidn}­vis|}lƒ‰m¨y3vigis`˜ndnuP¿¥‚ewldŠvih*vibld ¤[yY˜Pvqvxbly3vqvxbldŠƒ gihYwlfIg’s|}lƒ*hY¤y*u’wljlƒ g’h wlfÏs`}IƒYdn}ldPgxyYk ‚lhAdPu+}ehYvy3k|k|hS¦ y$˜Ph }­r dP}ls|dP}›v‚ldnu’˜ngis`fevxs`h }Šs|} vxbld¡uxyYmŠd¡flgihC‚lwl˜vhY¤¯m¨y{vxgis”

(114) g’s|}lƒ u hSr dPg¬Ó ¦ s|}­vxh ¦¬bls|˜šbÓ ¦ ¹NÔ g s`ucdnm„j0dn‚l‚edn‚^+¼zh guihYmdqgidPflgidPuidP}›vis|}lƒŠmy3vxg’s|˜ndPun¿e¦+d$gidP¤¹dPgcvxh‰ÛßÉ ~ Ü^ |ª˜9Óǘ} }. . ԋÏ~ œ*€d™d› Ô ¡~˜A™5œN5˜¢› }. . 6r. 8y z. o. . . . . #. . 8s. s. . . jz m. Kr. jz m. Kr. h . 9. 8s s h . . 9. „. . h. . sƒt. r‚. jz m. . 9. h. sƒt. #. . 9. . „. n. . #. 6#. 7#. Wc. 7y k. k Ko„. #. . #. . !$#. h ,. . %,. !$#. #. . 0. h. !$#. 9. %,. !$#. #. . #. . ')(‡†. 9. ˆ. /‰©/ŠFŠFEHCŒ‹. 4i. 132ŽEt:. /. 1 4‚. #. /;2ŽŠ. d ¦y3}›v$vxh*u’vigidPuiuj­¢ŸyY}Id Af0dngis`mdP}­v$vibldŠ}ldn˜Pdnuiu’s`v£¢Y¿?dPrYdn}Ϥ¹h gqh g’‚ls|}lyYg’¢mŠhC‚lwlk¾y3g—gidPflgidPuidn}C© všy3vis|h }vxbldPh g’¢Y¿¯hY¤&vibldfegis|mŠd$f7hS¦+dngiu®hA˜P˜nwlg’gis|}eƒ¨s|}*vxbld$vxs`dnu®g’dnu’f^¯s`}‰vxbedmŠhA‚lwek¾yYg¬mŠh giflbes|uimŠu dPr hY™Cs`}lƒvxbld9vis|dPun^Ïð£}%ƒ dP}ldngiyYkß¿&˜šblyY}lƒ s`}lƒ vxbld#fegis|mŠd9f0hS¦dPgiu

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