On maximal primitive quotients of infinitesimal Cherednik algebras of gl_n

TL;DR

This paper establishes analogues of Kostant's theorems for infinitesimal Cherednik algebras of gl_n, revealing that in positive characteristic, the Azumaya and smooth loci of their centers coincide, advancing understanding of their structure.

Contribution

It introduces analogues of Kostant's theorems for these algebras and characterizes the relationship between Azumaya and smooth loci in positive characteristic.

Findings

Azumaya and smooth loci of the center coincide in positive characteristic

Analogues of Kostant's theorems are established for these algebras

Provides structural insights into infinitesimal Cherednik algebras of gl_n

Abstract

We prove analogues of some of Kostant's theorems for infinitesimal Cherednik algebras of gl_n. As a consequence, it follows that in positive characteristic the Azumaya and smooth loci of the center of these algebras coincide.