Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 107, 13 pages      arXiv:1907.13417      https://doi.org/10.3842/SIGMA.2020.107

Quasi-Invariants in Characteristic $p$ and Twisted Quasi-Invariants

Michael Ren a and Xiaomeng Xu b
a)  Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
b)  School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China

Received July 10, 2020, in final form October 17, 2020; Published online October 27, 2020

Abstract
The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 were computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521-545]. In this paper, we show some partial results and make two conjectures on the Hilbert series of these spaces over fields of positive characteristic. On the other hand, Braverman, Etingof and Finkelberg [arXiv:1611.10216] introduced the spaces of quasi-invariant polynomials twisted by a monomial. We extend some of their results to the spaces twisted by a smooth function.

Key words: quasi-invariant polynomials; twisted quasi-invariants.

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References

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