mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Demazure conjecture is a conjecture about representations of algebraic groups over the integers made by . The conjecture implies that many of the results of his paper can be extended from complex algebraic groups to algebraic groups over

fields Fields may refer to: Music *Fields (band), an indie rock band formed in 2006 *Fields (progressive rock band), a progressive rock band formed in 1971 * ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010) * "Fields", a song by ...

of other characteristics or over the integers. showed that Demazure's conjecture (for classical groups) follows from their work on

standard monomial theory In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of elements called standard monomials. Many of th ...

, and

Peter Littelmann Peter Littelmann (born 10 December 1957) is a German mathematician at the University of Cologne working on algebraic groups and representation theory, who introduced the Littelmann path model and used it to solve several conjectures in standard m ...

extended this to all reductive algebraic groups.

References

* *{{cite 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 , series=New Series , issn=0002-9904 , volume=1 , issue=2 , pages=432–435, doi-access=free Representation theory Conjectures