Quasiinvariants of S3

被引：2
|
作者：
Bandlow, J [1 ]
Musiker, G [1 ]
机构：
[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2005年 / 109卷 / 02期
关键词：
m-quasiinvariants; symmetric group; symmetric functions; determinant evaluations; binomial coefficients; non-intersecting lattice paths;
D O I：
10.1016/j.jcta.2004.09.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let s(ij) represent a transposition in S-n. A polynomial P in Q[X-n] is said to be m-quasiinvariant with respect to S-n if (x(i) - x(j))(2m+1) divides (1 - s(ij)) P for all 1 <= i, j <= n. We call the ring of m-quasiinvariants, QI(m) [X-n], We describe a method for constructing a basis for the quotient QI(m) [X-3]/ (e(1), e(2), e(3)). This leads to the evaluation of certain binomial determinants that are interesting in their own right. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：281 / 298
页数：18
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