Mathematics Colloquia and Seminars

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The RSK bijection is one of the cornerstones of the combinatorics of the symmetric groups with many consequences that are important both for Combinatorics and for Representation Theory. For example, a classical application is to partition S_n into left cells, right cells and two-sided cells that is important for several problems in Representation Theory. A less classical application is to use the Schutzenberger involution on the standard Young tableaux to define two commuting actions of the so called cactus group (that should be thought as a crystal analog of the braid group) on S_n . These actions are nicely compatible with cells. I will start by explaining these constructions for the symmetric groups and then generalize cells, RSK correspondence and cacti actions to arbitrary Weyl groups.