• Corpus ID: 246016442

Toward explicit Hilbert series of quasi-invariant polynomials in characteristic $p$ and $q$-deformed quasi-invariants

@inproceedings{Wang2022TowardEH,
  title={Toward explicit Hilbert series of quasi-invariant polynomials in characteristic \$p\$ and \$q\$-deformed quasi-invariants},
  author={Frank Wang},
  year={2022}
}
We study the spaces Qm of m-quasi-invariant polynomials of the symmetric group Sn in characteristic p. Using the representation theory of the symmetric group we describe the Hilbert series of Qm for n = 3, proving a conjecture of Ren and Xu [10]. From this we may deduce the palindromicity and highest term of the Hilbert polynomial and the freeness of Qm as a module over the ring of symmetric polynomials, which are conjectured for general n. We also prove further results in the case n = 3 that… 

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