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Cacti and cells

Algebra & Discrete Mathematics

Speaker: Ivan Losev, Northeastern
Location: 1147 MSB
Start time: Mon, Mar 14 2016, 1:10PM

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.