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Theoretical and Mathematical Physics

, Volume 198, Issue 2, pp 249–255 | Cite as

Traces and Supertraces on Symplectic Reflection Algebras

  • S. E. KonsteinEmail author
  • I. V. Tyutin
Article
  • 5 Downloads

Abstract

The symplectic reflection algebra H1,ν (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 ν. We present values of T(G) and S(G) for the groups generated by the root systems and for the groups G = Γ ≀ SN, where Γ is a finite subgroup of Sp(2,ℂ).

Keywords

symplectic reflection algebra Cherednik algebra trace supertrace 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lebedev Physical InstituteRASMoscowRussia
  2. 2.Tomsk State Pedagogical UniversityTomskRussia

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