This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain results on ad-nilpotent ideals which complete the analysis started in (J. Algebra 225 (2000) 130, 258 (2002) 112). (C) 2003 Elsevier Inc. All rights reserved.
Abelian ideals of Borel subalgebras and affine Weyl groups / Papi, Paolo; Paola, Cellini. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 187:2(2004), pp. 320-361. [10.1016/j.aim.2003.08.011]
Abelian ideals of Borel subalgebras and affine Weyl groups
PAPI, Paolo;
2004
Abstract
This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain results on ad-nilpotent ideals which complete the analysis started in (J. Algebra 225 (2000) 130, 258 (2002) 112). (C) 2003 Elsevier Inc. All rights reserved.File allegati a questo prodotto
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