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 ''Representations'' is an interdisciplinary journal in the humanities published quarterly by the University of California Press. The journal was established in 1983 and is the founding publication of the New Historicism movement of the 1980s. It ...

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s 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 group In mathematics, the classical groups are defined as the special linear groups over the reals , the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or ske ...

s) 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 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