Multiparameter quantum Pfaffians

TL;DR

This paper introduces and studies the multiparameter quantum Pfaffian within the framework of $(p, \lambda)$-quantum groups, exploring its relation to quantum determinants and generalizations.

Contribution

It presents the first detailed study of the multiparameter quantum Pfaffian and its connections to quantum determinants and hyper-Pfaffians in quantum group theory.

Findings

Defined the multiparameter quantum Pfaffian for $(p, \lambda)$-quantum groups

Established an identity relating quantum Pfaffian and quantum determinant

Explored generalizations to hyper-Pfaffians and connections with quantum minors

Abstract

The multiparameter quantum Pfaffian of the $(p, \lambda)$-quantum group is introduced and studied together with the quantum determinant, and an identity relating the two invariants is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also considered.