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• W2950553984 abstract "We consider a filtration of the symmetric function space given by $Lambda^{(k)}_t$, 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 $Lambda^{(k)}_t$. 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 $Lambda^{(k)}_t$ 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." @default.
• W2950553984 created "2019-06-27" @default.
• W2950553984 creator A5025080862 @default.
• W2950553984 creator A5070901277 @default.
• W2950553984 date "2001-11-17" @default.
• W2950553984 modified "2023-09-27" @default.
• W2950553984 title "Schur function analogs for a filtration of the symmetric function space" @default.
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• W2950553984 hasPublicationYear "2001" @default.
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