کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4654471 1632845 2006 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Combinatorics of crystal graphs and Kostka–Foulkes polynomials for the root systems Bn,CnBn,Cn and DnDn
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Combinatorics of crystal graphs and Kostka–Foulkes polynomials for the root systems Bn,CnBn,Cn and DnDn
چکیده انگلیسی

We use Kashiwara–Nakashima combinatorics of crystal graphs associated with the roots systems BnBn and DnDn to extend the results of Lecouvey [C. Lecouvey, Kostka–Foulkes polynomials, cyclage graphs and charge statistics for the root system CnCn, J. Algebraic Combin. (in press)] and Morris [A.-O. Morris, The characters of the group GL(n,q)GL(n,q), Math. Z. 81 (1963) 112–123] by showing that Morris-type recurrence formulas also exist for the orthogonal root systems. We derive from these formulas a statistic on Kashiwara–Nakashima tableaux of types Bn,CnBn,Cn and DnDn generalizing the Lascoux–Schützenberger charge and from which it is possible to compute the Kostka–Foulkes polynomials Kλ,μ(q)Kλ,μ(q) under certain conditions on (λ,μ)(λ,μ). This statistic is different from that obtained in Lecouvey [C. Lecouvey, Kostka–Foulkes polynomials, cyclage graphs and charge statistics for the root system CnCn, J. Algebraic Combin. (in press)] from the cyclage graph structure on tableaux of type CnCn. We show that such a structure also exists for the tableaux of types BnBn and DnDn but cannot be related in a simple way to the Kostka–Foulkes polynomials. Finally we give explicit formulas for Kλ,μ(q)Kλ,μ(q) when |λ|≤3|λ|≤3, or n=2n=2 and μ=0μ=0.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 27, Issue 4, May 2006, Pages 526–557
نویسندگان
,