[{"key":"dc.contributor.author","value":"Schilling, Anne","language":null},{"key":"dc.date.accessioned","value":"2017-11-12T06:00:41Z","language":null},{"key":"dc.date.available","value":"2017-11-11T22:00:41","language":null},{"key":"dc.date.issued","value":"2017-05-15T11:29","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-201705151129-Schilling","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-17w5012-22121","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/63583","language":null},{"key":"dc.description.abstract","value":"Crystal bases were first introduced as a combinatorial tool to understand representations of quantum groups. They can also be understood from a purely combinatorial point of view (see for example the\nnew book by Bump and Schilling\non \"Crystal bases: Representations and Combinatorics\"). In particular, the\ncharacter of a connected crystal in type A is a Schur function. Hence, knowing\nthe crystal structure on a set that underlies a given symmetric function, will\nyield the Schur expansion of this symmetric function provided that the expansion\nis Schur-positive.\n\nAs an example, Brendon Rhoades in his article \u201cOrdered set partition statistics\nand the Delta conjecture\u201d investigated the symmetric functions Val_{n,k}(x;0,q).\nThese symmetric functions are Schur-positive (see page 19 of Rhoades' article).\nIt would be interesting to find a crystal structure on the ordered multiset\npartitions that define these symmetric functions.\n\nCrystal bases are very well developed in the open source computer algebra\nsystem Sage. So it should be easy to experiment with these structures in Sage.\n\nReferences:\n\n* Brendon Rhoades, Ordered set partition statistics and the Delta conjecture arXiv:1605.04007\n* Sage \n* Daniel Bump, Ben Salisbury, Anne Schilling Thematic Tutorial: Lie Methods and Related Combinatorics in Sage ","language":null},{"key":"dc.format.extent","value":"27 minutes","language":null},{"key":"dc.format.mimetype","value":"video\/mp4","language":null},{"key":"dc.language.iso","value":"eng","language":null},{"key":"dc.publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","language":null},{"key":"dc.relation","value":"17w5012: Algebraic Combinatorixx 2","language":null},{"key":"dc.relation.ispartofseries","value":"BIRS Workshop Lecture Videos (Banff, Alta)","language":null},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":null},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":null},{"key":"dc.subject","value":"Mathematics","language":null},{"key":"dc.subject","value":"Combinatorics","language":null},{"key":"dc.subject","value":"Group theory and generalizations","language":null},{"key":"dc.title","value":"Schur Expansions Via Crystal Bases","language":null},{"key":"dc.type","value":"Moving Image","language":null},{"key":"dc.description.affiliation","value":"Non UBC","language":null},{"key":"dc.description.reviewstatus","value":"Unreviewed","language":null},{"key":"dc.description.notes","value":"Author affiliation: University of California Davis","language":null},{"key":"dc.description.scholarlevel","value":"Faculty","language":null},{"key":"dc.date.updated","value":"2017-11-12T06:00:41Z","language":null}]