An algebraic cell decomposition of the nonnegative part of a flag variety

JOURNAL OF ALGEBRA

卷:213

Article

Rietsch, K

关键词: flag varieties;    linear algebraic groups;    total positivity;   

DOI  :  10.1006/jabr.1998.7665

来源: Elsevier

【 摘 要 】

We study the nonnegative part B-greater than or equal to 0 of the flag variety B of a reductive algebraic group, as defined by Lusztig. Using positivity properties of the canonical basis it is shown that B-greater than or equal to 0 has an algebraic cell decomposition indexed by pairs of elements w less than or equal to w' of the Weyl group. This result was conjectured by G. Lusztig (1994, in Progr. Math., Vol. 123, pp. 531-568, Birkhauser, Basel). (C) 1999 Academic Press.

【 授权许可】

Free