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Mosc. Math. J., 2003, Volume 3, Number 4, Pages 1269–1291 (Mi mmj131)  

This article is cited in 9 scientific papers (total in 10 papers)

Action of Coxeter groups on $m$-harmonic polynomials and Knizhnik–Zamolodchikov equations

G. Feldera, A. P. Veselovbc

a Departement für Mathematik, Eidgenösische Technische Hochschule Zürich
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Loughborough University

Abstract: The Matsuo–Cherednik correspondence is an isomorphism from solutions of Knizhnik–Zamolodchikov equations to eigenfunctions of generalized Calogero–Moser systems associated to Coxeter groups $G$ and a multiplicity function m on their root systems. We apply a version of this correspondence to the most degenerate case of zero spectral parameters. The space of eigenfunctions is then the space Hm of $m$-harmonic polynomials. We compute the Poincaré polynomials for the space Hm and for its isotypical components corresponding to each irreducible representation of the group $G$. We also give an explicit formula for m-harmonic polynomials of lowest positive degree in the $S_n$ case.

Key words and phrases: Coxeter groups, $m$-harmonic polynomials, Knizhnik–Zamolodchikov equation.

DOI: https://doi.org/10.17323/1609-4514-2003-3-4-1269-1291

Full text: http://www.ams.org/.../abst3-4-2003.html
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MSC: 13A50, 20F55
Received: July 9, 2002
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Citation: G. Felder, A. P. Veselov, “Action of Coxeter groups on $m$-harmonic polynomials and Knizhnik–Zamolodchikov equations”, Mosc. Math. J., 3:4 (2003), 1269–1291

Citation in format AMSBIB
\Bibitem{FelVes03}
\by G.~Felder, A.~P.~Veselov
\paper Action of Coxeter groups on $m$-harmonic polynomials and Knizhnik--Zamolodchikov equations
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 4
\pages 1269--1291
\mathnet{http://mi.mathnet.ru/mmj131}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-4-1269-1291}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2058799}
\zmath{https://zbmath.org/?q=an:1056.32013}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208594400004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Berest Y., Etingof P., Ginzburg V., “Cherednik algebras and differential operators on quasi-invariants”, Duke Math J, 118:2 (2003), 279–337  crossref  mathscinet  zmath  isi
    2. M. V. Feigin, “Quasi-Invariants of Dihedral Systems”, Math. Notes, 76:5 (2004), 723–737  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Felder G., Veselov A.P., “Polynomial Solutions of the Knizhnik–Zamolodchikov Equations and Schur-Weyl Duality”, International Mathematics Research Notices, 2007, rnm046  mathscinet  zmath  isi  elib
    4. Bandlow J., Musiker G., “A new characterization for the m-quasiinvariants of S-n and explicit basis for two row hook shapes”, Journal of Combinatorial Theory Series A, 115:8 (2008), 1333–1357  crossref  mathscinet  zmath  isi
    5. Tsuchida T., “On Quasiinvariants of $S_n$ of Hook Shape”, Osaka J Math, 47:2 (2010), 461–485  mathscinet  zmath  isi  elib
    6. Finkelberg M., Ginzburg V., “On Mirabolic D-modules”, Int Math Res Not, 2010, no. 15, 2947–2986  crossref  mathscinet  zmath  isi  elib
    7. Berest Yu., Chalykh O., “Quasi-invariants of complex reflection groups”, Compos Math, 147:3 (2011), 965–1002  crossref  mathscinet  zmath  isi  elib
    8. Feigin M. Johnston D., “a Class of Baker-Akhiezer Arrangements”, Commun. Math. Phys., 328:3 (2014), 1117–1157  crossref  mathscinet  zmath  isi  elib
    9. V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1159–1176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. B. Zegarliński, “Crystallographic Groups for Hörmander Fields”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:3 (2017), 43–64  mathnet  crossref
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