On the Standard Expression for the Party Algebra(The world of Combinatorial Representation Theory)
Masashi Kosuda · Institutional Repositories DataBase (IRDB) · 2006
In this note we explain about the party algebra $P_{n,r}(Q)$ and its standard ex- pression.The party algebra is originally defined as the centralizer of the unitary reflection group of type $G(r, 1, k)$ which diagonally acts on the $n$ times tensor space $V^{\otimes n}$ .This algebra is also defined as a diagram algebra like Temperly- Lieb's algebra, Brauer's centralizer algebra, the partition algebra, and so on.It is well known that these diagram algebras have the cellular structures.The cellular structure of an algebra tells that how the algebra's basis is decomposed into the cells, which may turn out to be the representatives of the irreducible representations.