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Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1947

Title: Schur function analogs for a filtration of the symmetric function space
Authors: Morse, Jennifer
Lapointe, Luc
Issue Date: 17-Nov-2001
Citation: Retrieved November 2, 2007 from http://xxx.lanl.gov/find/grp_math/1/au:+Morse_J/0/1/0/all/0/1.
Abstract: We consider a filtration of the symmetric function space given by At(k) , the linear span of Hall-Littlewood polynomials indexed by partitions whose first part is not larger than k. We introduce symmetric functions called the k-Schur functions, providing an analog for the Schur functions in the subspaces At(k) . We prove several properties for the k-Schur functions including that they form a basis for these subspaces that reduces to the Schur basis when k is large. We also show that the connection coefficients for the k-Schur function basis with the Macdonald polynomials belonging to At(k) are polynomials in q and t with integral coefficients. In fact, we conjecture that these integral coefficients are actually positive, and give several other conjectures generalizing Schur function theory.
URI: http://lanl.arxiv.org/abs/math/0111192v1
Appears in Collections:Faculty Research and Publications (Mathematics)

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