Fusion Procedure for Cyclotomic Hecke Algebras

TL;DR

This paper introduces a method to explicitly construct primitive orthogonal idempotents in cyclotomic Hecke algebras using evaluations of a specialized rational function related to multi-tableaux and Schur elements.

Contribution

It provides a complete explicit construction of primitive idempotents in cyclotomic Hecke algebras, advancing the algebraic understanding of their structure.

Findings

Explicit formula for primitive idempotents via rational function evaluations

Connection established between idempotents, multi-tableaux, and Schur elements

Method applicable to various cyclotomic Hecke algebras

Abstract

A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a product of two terms, one of which depends only on the shape of the multi-tableau and is proportional to the inverse of the corresponding Schur element.