De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum gl_N

Abstract

In this note we compute the leading term with respect to the De Concini-Kac filtration of $U_q({\mathfrak{gl}}_n)$ of a generating set for the quantum Gelfand-Tsetlin subalgebra.

arXiv comment12 pages. v2: The statement about the quantum Gelfand-Tsetlin subalgebra being maximal commutative has been removed as an error was found in the proof

References in corpus (3)

• A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
• Solution of a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl_N
• Fibers of characters in Harish-Chandra categories

Cited by in corpus (2)

• Gelfand-Tsetlin modules of quantum gl_n$defined by admissible sets of relations
• Explicit construction of irreducible modules for U_q(gl_n)