The center of the small quantum group u_q(sl_3) for l=5: a numerical computation

TL;DR

This paper presents a numerical computation of the center's dimension for the small quantum group u_q(sl_3) at a 5th root of unity, providing detailed block decomposition insights.

Contribution

It offers the first detailed numerical analysis of the center's structure and block decomposition for u_q(sl_3) at l=5, expanding understanding of its algebraic properties.

Findings

Center's dimension is 57 at l=5

Singular parabolic block dimension is 6

Complete block decomposition of the center obtained

Abstract

This is a brief note on a numerical computation of the dimension of the center of the small quantum group u_q(sl_3) at the 5th root of unity. The obtained dimension is 57. Using the description of the regular block of the center for u_q(sl_3), given in arXiv:1604.07380, we conclude that the dimension of the singular parabolic block of the center for u_q(sl_3) is 6, and obtain a complete block decomposition of the center in this case.