2024-03-28T20:39:46Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696282022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Garsia-Haiman modules for hook partitions and Green polynomials with two variablesMorita, HideakiSymmetric groupsGarsia-Haiman modulesGreen polynomials with two variablesMacdonald polynomialsRoots of unity410We consider Garsia-Haiman modules for the symmetric groups, a doubly graded generalization of Springer modules. Our main interest lies in singly graded submodules of a Garsia-Haiman module. We show that these submodules satisfy a certain combinatorial property, and verify that this property is implied by a behavior of Macdonald polynomials at roots of unity.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69628info:doi/10.14943/83970https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69628/1/pre820.pdfHokkaido University Preprint Series in Mathematics8201132006engpublisher