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Schur function analogs for a filtration of the symmetric function space
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1860/1947
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| 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
http://hdl.handle.net/1860/1947 |
| Appears in Collections: | Faculty Research and Publications (Mathematics)
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