An insertion algorithm on multiset partitions with applications to diagram algebras

JOURNAL OF ALGEBRA

卷:557

Article

Colmenarejo, Laura¹  Orellana, Rosa²  Saliola, Franco³  Schilling, Anne⁴  Zabrocki, Mike⁵ 

[1] UMass Amherst, Dept Math & Stat, 710 N Pleast St, Amherst, MA 01003 USA

[2] Dartmouth Coll, Math Dept, 6188 Kemeny Hall, Hanover, NH 03755 USA

[3] Univ Quebec Montreal, Dept Math, Montreal, PQ, Canada

[4] Univ Calif Davis, Dept Math, One Shields Ave, Davis, CA 95616 USA

[5] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada

关键词: Partition algebras;    RSK algorithm;    Multiset tableaux;    Representation theory;   

DOI  :  10.1016/j.jalgebra.2020.04.010

来源: Elsevier

【 摘 要 】

We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer algebras and the spaces they act on. In addition, restrictions on the multisets lead to further identities and representation theory analogues. For instance, we obtain a bijection between words of length k with entries in [n] and pairs of tableaux of the same shape with one being a standard Young tableau of size n and the other being a standard multiset tableau of content [k]. We also obtain an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic results of Halverson and Jacobson [15]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free