Infinitesimal Hecke algebras of so_N

TL;DR

This paper classifies all infinitesimal Hecke algebras associated with so_N and relates their universal forms to W-algebras of specific nilpotent types, extending previous work on gl_n and sp_{2n}.

Contribution

It provides a complete classification of infinitesimal Hecke algebras of so_N and establishes isomorphisms with certain W-algebras, advancing the understanding of their structure.

Findings

Classified all infinitesimal Hecke algebras of so_N.

Established isomorphisms with W-algebras of so_{N+2m+1}.

Extended previous results from gl_n and sp_{2n} cases.

Abstract

In this article we classify all infinitesimal Hecke algebras of so_N. We establish isomorphism of their universal versions and the W-algebras of so_{N+2m+1} with a 1-block nilpotent element of the Jordan type (1,...,1,2m+1). This should be considered as a continuation of the recent joint paper with I. Losev, where the analogous results were obtained for the cases of gl_n and sp_{2n}.