Geodesic
Super multiset RSK and a mixed multiset partition algebra
Alexander Wilson1
1Oberlin College
The electronic journal of combinatorics, Tome 31 (2024) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

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 that 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.
DOI : 10.37236/12807
Classification : 05E10, 20C30, 20G05
Mots-clés : Robinson-Schensted-Knuth algorithm, representation theory of the symmetric group

Alexander Wilson  1

1 Oberlin College 
@article{10_37236_12807,
     author = {Alexander Wilson},
     title = {Super multiset {RSK} and a mixed multiset partition algebra},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12807},
     zbl = {1556.05169},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12807/}
}
TY  - JOUR
AU  - Alexander Wilson
TI  - Super multiset RSK and a mixed multiset partition algebra
JO  - The electronic journal of combinatorics
PY  - 2024
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/12807/
DO  - 10.37236/12807
ID  - 10_37236_12807
ER  - 
%0 Journal Article
%A Alexander Wilson
%T Super multiset RSK and a mixed multiset partition algebra
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12807/
%R 10.37236/12807
%F 10_37236_12807
Alexander Wilson. Super multiset RSK and a mixed multiset partition algebra. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12807

Cité par Sources :