• Corpus ID: 119582365

Shifted Schur Functions

@article{Okounkov1996ShiftedSF,
  title={Shifted Schur Functions},
  author={Andrei Okounkov and Grigori Olshanski},
  journal={arXiv: Quantum Algebra},
  year={1996}
}
The classical algebra $\Lambda$ of symmetric functions has a remarkable deformation $\Lambda^*$, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a distinguished basis formed by shifted Schur functions $s^*_\mu$, where $\mu$ ranges over the set of all partitions. The main significance of the shifted Schur functions is that they determine a natural basis in $Z(\frak{gl}(n))$, the center of the universal enveloping algebra $U(\frak{gl}(n))$, $n=1,2,\ldots… 

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