Party algebra and construction of its irreducible representations

Masashi KOSUDA

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


Suppose that there exist two parties each of which consists of $n$ members. The parties hold meetings splitting into several small groups. Every group consists of the same number of members of each party. The set of such decompositions into small groups makes an algebra called {\em the party algebra} under a certain product. We show that the party algebra is semisimple by constructing a complete set of irreducible representations.

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