Geodesic
Traces and supertraces on the~symplectic reflection algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 2, pp. 284-291

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The symplectic reflection algebra $H_{1,\nu}(G)$ has a $T(G)$-dimensional space of traces, and if it is regarded as a superalgebra with a natural parity, then it has an $S(G)$-dimensional space of supertraces. The values of $T(G)$ and $S(G)$ depend on the symplectic reflection group $G$ and are independent of the parameter $\nu$. We present values of $T(G)$ and $S(G)$ for the groups generated by the root systems and for the groups $G=\Gamma\wr S_N$, where $\Gamma$ is a finite subgroup of $Sp(2,\mathbb C)$.
Keywords: symplectic reflection algebra, Cherednik algebra, trace
Mots-clés : supertrace. 
@article{TMF_2019_198_2_a5,
     author = {S. E. Konstein and I. V. Tyutin},
     title = {Traces and supertraces on the~symplectic reflection algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {284--291},
     publisher = {mathdoc},
     volume = {198},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_2_a5/}
}
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S. E. Konstein; I. V. Tyutin. Traces and supertraces on the~symplectic reflection algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 2, pp. 284-291. http://geodesic.mathdoc.fr/item/TMF_2019_198_2_a5/