I. G. MacDonald

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for making many comments and corrections concerning these notes. All rings are commutative and contain multiplicative identity, moreover we will always insist that ring homomorphisms respect the multiplicative identity element. Local rings are assumed to be Noetherian. Additionally, all modules are unitary modules. We have made an attempt to be consistent(More)
In this article we shall survey various generalizations, analogues and deformations of Schur functions — some old, some new — that have been proposed at various times. We shall present these as a sequence of variations on a theme and (unlike e.g. Bourbaki) we shall proceed from the particular to the general. Thus Variations 1 and 2 are included in Variation(More)
Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W , such that S (but not necessarily R) is reduced. For each such pair (R, S) we construct a family of W -invariant orthogonal polynomials in several variables, whose coefficients are rational functions of parameters q, t1, t2, . . . , tr, where r (= 1,(More)
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