Séminaire Lotharingien de Combinatoire, 78B.59 (2017), 12 pp.

Motoki Takigiku

On Some Factorization Formulas of K-k-Schur Functions

Abstract. We give some new formulas about factorizations of K-k-Schur functions g(k)λ, analogous to the k-rectangle factorization formula s(k)Rt u λ = s(k)Rt s(k)λ of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (tk+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that g(k)Rt divides g(k)Rt u λ, and in fact more generally that g(k)P divides g(k)P u λ for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such g(k)P and explicit formulas for g(k)P u λ / g(k)P in some cases.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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