ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration
Rings and Algebras
2007-05-23 v1 Combinatorics
Abstract
We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of . We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. We study the relationships between these results and the combinatorics of Dyck paths, based upon a remarkable bijection between ad-nilpotent ideals and Dyck paths. Finally, we propose a (q,t)-analogue of the Catalan number . These (q,t)-Catalan numbers count on the one hand ad-nilpotent ideals with respect to dimension and class of nilpotence, and on the other hand admit interpretations in terms of natural statistics on Dyck paths.
Keywords
Cite
@article{arxiv.math/0004107,
title = {ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration},
author = {George E. Andrews and Christian Krattenthaler and Luigi Orsina and Paolo Papi},
journal= {arXiv preprint arXiv:math/0004107},
year = {2007}
}
Comments
19 pages, AmS-TeX