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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 |
| Related Webpage: | https://www.scu.edu/mathcs/faculty-and-staff/tamsen-mcginley/mcginley.html |
| 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.