Mathematical Journal of Okayama University volume64 issue1
2022-01 発行

Quantum Sylvester-Franke Theorem

Aokage, Kazuya Department of Mathematics, National Institute of Technology, Ariake College
Tabata, Sumitaka Department of Mathematics, Kumamoto University
Yamada, Hiro-Fumi Department of Mathematics, Kumamoto University
Publication Date
2022-01
Abstract
A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally
Keywords
Quantum general linear group
Sylvester-Franke theorem
Comments
Mathematics Subject Classification. Primary 20G42; Secondary 81R50.