Schur function analogs for a filtration of the symmetric function space

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dc.creatorLapointe, L.
dc.creatorMorse, J.
dc.date2001-11-17
dc.date.accessioned2026-07-07T04:44:38Z
dc.date.available2026-07-07T04:44:38Z
dc.descriptionWe consider a filtration of the symmetric function space given by $Λ^{(k)}_t$, 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 $Λ^{(k)}_t$. 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 $Λ^{(k)}_t$ 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.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0111192
dc.identifierhttp://arxiv.org/abs/math/0111192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62672
dc.subjectCombinatorics
dc.subject05E05
dc.titleSchur function analogs for a filtration of the symmetric function space
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