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arXiv · 1505.07891

The polynomial representation of the type $A_{n - 1}$ rational Cherednik algebra in characteristic $p \mid n$

Sheela Devadas·Yi Sun
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Abstract

We study the polynomial representation of the rational Cherednik algebra of type $A_{n-1}$ with generic parameter in characteristic $p$ for $p \mid n$. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic $p$ analogues of existing characteristic $0$ results.

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BibTeXRIS

Sheela Devadas, Yi Sun. 2015-05-29. The polynomial representation of the type $A_{n - 1}$ rational Cherednik algebra in characteristic $p \mid n$. https://doi.org/10.1080/00927872.2016.1226866

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