Paper
Coordinate rings of regular semisimple Hessenberg varieties and cohomology rings of regular nilpotent Hessenberg varieties
Authors
Tatsuya Horiguchi
Abstract
The polynomials are introduced by Abe-Harada-Horiguchi-Masuda to produce an explicit presentation by generators and relations of the cohomology rings of regular nilpotent Hessenberg varieties. In this paper we quantize the polynomials by a method of Fomin-Gelfand-Postnikov. Our main result states that their quantizations are related to the coordinate rings of regular semisimple Hessenberg varieties. This result yields a connection between the coordinate rings of regular semisimple Hessenberg varieties and the cohomology rings of regular nilpotent Hessenberg varieties. We also provide the quantized recursive formula for .