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AG Audience

English

30 Minutes

Saarbrücken

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on a straightening process, originally due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. All previously existing algorithms for straightening a filling have been iterative processes and it has been a long-standing open problem to give a non-iterative algorithm. In this talk I will provide such an algorithm, as well as a simple combinatorial description of the coefficients that arise. This non-iterative method is both more useful for proofs and considerably more efficient than the classical straightening algorithms. I will cover all the combinatorial background necessary for this topic, the only prerequisite is some basic linear algebra.

Reuven Hodges

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straightening; Young diagrams; tableau; representation theory