Fusion procedure for cyclotomic BMW algebras

TL;DR

This paper develops a fusion procedure to explicitly construct orthogonal primitive idempotents in generic cyclotomic BMW algebras using rational functions, extending similar results to Nazarov-Wenzl algebras.

Contribution

It introduces a new fusion method for constructing primitive idempotents in cyclotomic BMW algebras, generalizing previous work and including Nazarov-Wenzl algebras.

Findings

Primitive idempotents constructed via rational function evaluations

Fusion procedure applicable to cyclotomic BMW algebras

Extension of results to Nazarov-Wenzl algebras

Abstract

Inspired by the work [IMOg2], in this note, we prove that the pairwise orthogonal primitive idempotents of generic cyclotomic Birman-Murakami-Wenzl algebras can be constructed by consecutive evaluations of a certain rational function. In the appendix, we prove a similar result for generic cyclotomic Nazarov-Wenzl algebras.