Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Discrete Mathematics and Combinatorics
The Multiset Partition Algebra: Diagram-Like Bases And Representations, Alexander N. Wilson
The Multiset Partition Algebra: Diagram-Like Bases And Representations, Alexander N. Wilson
Dartmouth College Ph.D Dissertations
There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur--Weyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset partition algebra. The partition algebra has a well-known basis indexed by graph-theoretic diagrams which allows the multiplication in the algebra to be understood visually as combinations of these diagrams. My thesis begins with a construction of an analogous basis for the multiset partition algebra. It continues with applications of this basis to constructing the irreducible …