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Perforated Tableaux - a combinatorial model for crystal graphs of type A_n

Algebra & Discrete Mathematics

Speaker: Tamsen (Whitehead) McGinley, Santa Clara University
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Location: 1147 MSB
Start time: Mon, Nov 25 2019, 12:10PM

Vertices of the standard A_n crystal graph are integers in [n] = {1, 2, . . . , n}. One can identify vertices in the crystal tensor product [n]^k. We replace words with perforated tableaux (ptableaux), and show how they can be used to simplify crystal operators, and identify highest weight elements (for all crystals directly). We generalize the tensor products in the Littlewood-Richardson rule to all of [n]^k, and relate evacuation (the Lusztig involution) to products of ptableaux crystal operators.