Ribbon Operators and Hall-Littlewood Symmetric Functions
نویسنده
چکیده
Abstract. Given a partition λ = (λ1, λ2, . . . λk), let λ rc = (λ2 − 1, λ3 − 1, . . . λk − 1). It is easily seen that the diagram λ/λ is connected and has no 2 × 2 subdiagrams which we shall refer to as a ribbon. To each ribbon R, we associate a symmetric function operator S. We may define the major index of a ribbon maj(R) to be the major index of any permutation that fits the ribbon. This paper is concerned with the operator H 1 = ∑ R q S where the sum is over all 2 ribbons of size k. We show here that H 1 has truly remarkable properties, in particular that it is a Rodriguez operator that adds a column to the Hall-Littlewood symmetric functions. We believe that some of the tools we introduce here to prove
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