ad-nilpotent ideals of a Borel subalgebra: generators and duality

Journal of Algebra - Tập 274 Số 2 - Trang 822-846 - 2004
Dmitri I. Panyushev1
1Independent University of Moscow, Bol'shoi Vlasevskii per. 11, 121002 Moscow, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

Andrews, 2002, ad-nilpotent b-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration, Trans. Amer. Math. Soc., 354, 3835, 10.1090/S0002-9947-02-03064-7

Athanasiadis, 1996, Characteristic polynomials of subspace arrangements and finite fields, Adv. Math., 122, 193, 10.1006/aima.1996.0059

Athanasiadis, 1998, On noncrossing and nonnesting partitions for classical reflection groups, Electron. J. Combin., 5, 10.37236/1380

C.A. Athanasiadis, Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes, Bull. London Math. Soc., submitted for publication

C.A. Athanasiadis, On a refinement of the generalized Catalan numbers for Weyl groups, Preprint, 2003, 18 pp

Bessis

Bonin, 1993, Some q-analogs of Shröder numbers arising from combinatorial statistics on lattice paths, J. Statist. Plann. Inference, 34, 35, 10.1016/0378-3758(93)90032-2

Cellini, 2000, ad-nilpotent ideals of a Borel subalgebra, J. Algebra, 225, 130, 10.1006/jabr.1999.8099

Cellini, 2002, ad-nilpotent ideals of a Borel subalgebra II, J. Algebra, 258, 112, 10.1016/S0021-8693(02)00532-X

Deutsch, 1999, Dyck path enumeration, Discrete Math., 204, 167, 10.1016/S0012-365X(98)00371-9

Fomin

Kostant, 1998, The set of abelian ideals of a Borel subalgebra, Cartan decompositions, and discrete series representations, Internat. Math. Res. Notices, 5, 225, 10.1155/S107379289800018X

Leung, 2002, The signature of a toric variety, Duke Math. J., 111, 253, 10.1215/S0012-7094-02-11123-5

Orsina, 2003, Enumeration of ad-nilpotent ideals of a Borel subalgebra in type A by class of nilpotence, C. R. Acad. Sci. Paris, Sér. Math., 330, 651, 10.1016/S0764-4442(00)00253-6

Panyushev, 2003, Abelian ideals of a Borel subalgebra and long positive roots, Internat. Math. Res. Notices, 1889, 10.1155/S1073792803211053

Reiner, 1997, Non-crossing partitions for classical reflection groups, Discrete Math., 177, 122, 10.1016/S0012-365X(96)00365-2

Sagan, 1999, Why the characteristic polynomial factors?, Bull. Amer. Math. Soc., 36, 113, 10.1090/S0273-0979-99-00775-2

Shi, 1997, The number of ⊕-sign types, Quart. J. Math. Oxford, 48, 93, 10.1093/qmath/48.1.93

Sommers

Stanley, 1997

Stanley, 1999

Stembridge, 1994, On minuscule representations, plane partitions, and involutions in complex Lie groups, Duke Math. J., 73, 469, 10.1215/S0012-7094-94-07320-1

Zaslavsky, 1975, Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc., 154