The polynomial representation of the type $A_{n  1}$ rational Cherednik algebra in characteristic $p \mid n$
Abstract
We study the polynomial representation of the rational Cherednik algebra of type $A_{n1}$ 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.07891
 Bibcode:
 2015arXiv150507891D
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra
 EPrint:
 8 pages. v3: Streamlined proof of complete intersection property in Section 3