
vittekkar model

ganithashaasthrathinte oru shaakhayaaya praathinidhya sidhaanthathil, groupile pravartthanangalude oru sthalathu parimithamaaya allengil praadeshika allengil aagola feeldil "jii. ell" 2 polulla oru reductive beejaganita grouppinte praathinidhyatthinte saakshaathkaaramaanu vittekkar model. iii yude perilaanu ithu ariyappedunnathu. tii. vittekkar orikkalum eee mekhalayil pravarthichittillengile, kaaranam groupinu sl2 (aarr) prathinidheekarikkunnathil ulppedunna chila pravartthanangal vittekkar pravarthanangalaanennu choondikkaanichu.
oru vittekkar model illaatha irreducible praathinidhyangale chilappol "degenerate" ennum vittekkar model ullavaye chilappol "generic" ennum vilikkunnu. symplectic group sp4-nte "θ" 10 enna praathinidhyam degenerate praathinidhyatthinte ettavum lalithamaaya udaaharanamaanu.
jii. ell. 2-nulla vittekkar modalukal.
g" ennathu beejaganita grouppaaya "gl" 2 umm f oru praadeshika feeld, f-nte additteev grouppinte oru nischitha noonn-trivial pratheekavum oru pothu leanier group "g" (f)-nte irreducible praathinidhyavumaanenkil, appol vittekkar model "g" (f) samthrupthikaramaaya functionukalude oru speysile praathinidyamaanu.
 jii. ell" 2-nte sveekaaryamaaya praathinidyangalkku ell-functionukal nalkaan vittekkar modalukal upayogichu.
jii. ell "enn"-nulla vittekkar modalukal.
formula 2 ennathu pothuvaaya leanier group formula 3 ayirikkatte, formula 4 ennathu formula 5-nte minusamarnna complexes moolyamulla noonn-trivial additteev pratheekavum formula 6 ennathu unipottant upper triangular maatriksukal adangiya formula 3-nte upavibhagavumaanu. formula _ 6-leeii oru degenerate cheyyaatha aksharam roopathilaanu
formula _ 10 ± formula _ 6, poojyamallaatha formula _ 12 ± formula _ 5 ennivaykku. formula _ 14 formula _ 15-nte sugamamaya praathinidhyamaanenkil, oru vittekkar functional formula _ 16 formula _ 17-leeii oru thudarchayaaya rekheeya pravarthanamaanu, athaayath formula _ 19 ± formula _ 6, formula _ 21 ± formula _ 17. gunithathil onnu prasthaavikkunnath, formula _ 23 unitory irreducible, vittekkar functionalukalude space paramavadhi onninu thulyamaanu.
reductive grouppukalkkulla vittekkar modalukal.
g" oru splitt reductive group "u" oru boral subgroup "b" yude unipottant raadikkalumaanenkil, oru praathinidhyathinaayulla oru vittekkar model athu induced (gelfand-grave) praathinidhyatthil ulcherkkunnathaanu, ivide "u" yude degenerate cheyyaatha pratheekamaanu, lalithamaaya verukalumaayi bandhapetta pratheekangalude koottam.