Demazure conjecture: Difference between revisions

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In [[mathematics]], the '''Demazure conjecture''' is a conjecture about [[group representation|representations]] of [[algebraic group]]s over the integers made by {{harvs|txt|last=Demazure|authorlink=Michel Demazure|year=1974|loc=p. 83}}. The conjecture implies that many of the results of his paper can be extended from complex algebraic groups to algebraic groups over [[field (mathematics)|fields]] of other characteristics or over the integers. {{harvs|txt | last1=Lakshmibai | first1=V. | last2=Musili | first2=C. | last3=Seshadri | first3=C. S. | title=Geometry of G/P | urldoi=https://dx.doi.org/10.1090/S0273-0979-1979-14631-7 | doi-access=10.1090/S0273-0979-1979-14631-7 free|mr=520081 | year=1979 | journal=Bulletin of the American Mathematical Society. Bulletin. |series=New Series | issn=0002-9904 | volume=1 | issue=2 | pages=432–435}} showed that Demazure's conjecture (for [[classical group]]s) follows from their work on [[standard monomial theory]], and [[Peter Littelmann]] extended this to all reductive algebraic groups.

==References==

*{{Citationcite journal |last1=Demazure |first1=Michel |author1-link=Michel Demazure |title=Désingularisation des variétés de Schubert généralisées |mr=0354697 |year=1974 |journal=Annales Scientifiques de l'École Normale Supérieure |series=Série 4 |issn=0012-9593 |volume=7 |pages=53–88|doi=10.24033/asens.1261 |doi-access=free }}

*{{Citationcite journal | last1=Lakshmibai | first1=V. | last2=Musili | first2=C. | last3=Seshadri | first3=C. S. | title=Geometry of G/P | doi=10.1090/S0273-0979-1979-14631-7 |mr=520081 | year=1979 | journal=Bulletin of the American Mathematical Society. Bulletin. |series=New Series | issn=0002-9904 | volume=1 | issue=2 | pages=432–435| doi-access=free }}

[[Category:Representation theory]]

[[Category:Conjectures]]