Quasiinvariants of S-3

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.