Super Multiset RSK and a Mixed Multiset Partition Algebra

Autor:	Wilson, Alexander
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Combinatorics 05E10 (Primary) 20C30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Through dualities on representations on tensor powers and symmetric powers respectively, the partition algebra and multiset partition algebra have been used to study long-standing questions in the representation theory of the symmetric group. In this paper we extend this story to exterior powers, introducing the mixed multiset partition algebra as well as a generalization of the Robinson-Schensted-Knuth algorithm to two-row arrays of multisets with elements from two alphabets. From this algorithm, we obtain enumerative results which reflect representation-theoretic decompositions of this algebra. Furthermore, we use the generalized RSK algorithm to describe the decomposition of a polynomial ring in sets of commuting and anti-commuting variables as a module over both the general linear group and the symmetric group. Comment: 28 pages, 12 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.07238 Zobrazit plný text záznamu View this record from Arxiv