XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019 VIII School on Geometry and Physics 24-28.06.2019
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# Alexander Sergeev

## On rings of supersymmetric polynomials

We consider three types of rings of supersymmetric polynomials: polynomial ones $\Lambda_{m,n}$, partially polynomial $\Lambda_{m,n}^{+y}$ and Laurent supersymmetric rings $\Lambda_{m,n}^{\pm}$. For each type of rings we give their descriptions in terms of generators and relations. As a corollary we get for $n\ge m$ an isomorphism $\Lambda_{m,n}^{+y}=\Lambda_{m,m}^{+y}\otimes\Lambda^{+y}_{0,n-m}$. It is also true for polynomial rings, but in this case the isomorphism does not preserve the grading. For each type of rings some natural basis consisting of Euler characters is constructed.

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