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This article is cited in 23 scientific papers (total in 23 papers)
On $m$-quasi-invariants of a Coxeter group
P. Etingofa, V. A. Ginzburgb a Department of Mathematics, Harvard University
b University of Chicago
Abstract:
Let $W$ be a finite Coxeter group in a Euclidean vector space $V$, and let m be a $W$-invariant $\mathbb Z_+$-valued function on the set of reflections in $W$. Chalykh and Veselov introduced an interesting algebra $Q_m$, called the algebra of $m$-quasi-invariants for $W$, such that $\mathbb C[V]_W\subseteq Q_m\subseteq\mathbb C[V]$, $Q_0=\mathbb C[V]$ and $Q_m\supseteq Q_{m'}$ whenever $m\leq m'$. Namely, $Q_m$ is the algebra of quantum integrals of the rational Calogero–Moser system with coupling constant $m$. Feigin and Veselov proposed a number of interesting conjectures concerning the structure of $Q_m$ and verified them for dihedral groups and constant functions $m$. Our objective is to prove some of these conjectures in the general case.
Key words and phrases:
Calogero–Moser system, Coxeter groups, $m$-quasi-invariants.
Received: March 2, 2002
Citation:
P. Etingof, V. A. Ginzburg, “On $m$-quasi-invariants of a Coxeter group”, Mosc. Math. J., 2:3 (2002), 555–566
Linking options:
https://www.mathnet.ru/eng/mmj63 https://www.mathnet.ru/eng/mmj/v2/i3/p555
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Abstract page: | 331 | References: | 63 |
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