The Haar State on SU_q(N)

TL;DR

This paper constructs a Haar state on the quantum group SU_q(N) using matrix corepresentations, enabling the creation of an orthonormal basis for its coordinate functions, extending methods from SU_q(2).

Contribution

It introduces a Haar state on SU_q(N) derived from matrix corepresentations, generalizing the approach used for SU_q(2).

Findings

Haar state on SU_q(N) closely resembles that on SU_q(2)

Established an orthonormal basis for coordinate functions on SU_q(N)

Extended matrix corepresentation techniques to higher dimensions

Abstract

Using matrix corepresentations on SL_q(N) and SU_q(N) we derive a Haar state on SU_q(N) which is nearly identical to that on SU_q(2). This allows us to create an orthonormal basis for the vector space of coordinate functions on SU_q(N).