| Start Date: | 11/10/2015 | Start Time: | 3:00 PM |
| End Date: | 11/10/2015 | End Time: | 4:00 PM |
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Event Description
Anna Pun, University of Pennsylvania Abstract: It is an open problem to prove the Schubert positivity property combinatorially. Recently Haglund, Mason, Remmel, van Willigenburg et al. have studied the skyline fillings (a tableau-combinatorial object giving a combinatorial description to nonsymmetric Macdonald polynomials , proved by Haglund, Haiman and Loehr) specifically for the case of Demazure atoms (atoms) and key polynomials (keys). This suggests a new approach to a combinatorial proof of Schubert positivity property. In this talk, I will introduce Demazure atoms and key polynomials using skyline fillings called semi-standard augmented fillings (SSAFs) and define generalized Demazure atoms by some modifications on SSAF defining atoms and keys. I will illustrate the insertion algorithm on Demazure atoms proved by Mason and describe refinements of Littlewood-Richardson rule proved by Haglund, Mason and Willigenburg. Then I will describe an algorithm to prove the atom positivity property of the product of a monomial and a Demazure atom. The last result gives positive support to the approach of the combinatorial proof of Schubert positivity property. |
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Location:
Korman Center, Room 245, 15 South 33rd Street, Philadelphia, PA 19104 |
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