Two relations for the antisymmetrizer in the Hecke algebra

TL;DR

This paper establishes two key relations for the antisymmetrizer in the Hecke algebra and explores their implications for the structure of unitary representations on tensor powers of complex n-space.

Contribution

It introduces two new relations for the antisymmetrizer in the Hecke algebra and analyzes their impact on unitary representations.

Findings

Derived restrictions on unitary representations from the relations

Identified algebraic properties of the antisymmetrizer in Hecke algebra

Enhanced understanding of the structure of tensor power representations

Abstract

We prove two relations for the antisymmetrizer in the Hecke algebra and derive certain restrictions imposed by these relations on unitary representations of the Hecke algebra on tensor powers of the space ${\mathbb C}^n$.