A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Kuniba, A., Okado, M., Yamada, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149342
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Common Structure in PBW Bases of the Nilpotent Subalgebra of Uq(g) and Quantized Algebra of Function / A. Kuniba, M. Okado, Y. Yamada // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 27 назв. — англ.

For a finite-dimensional simple Lie algebra g, let U⁺q(g) be the positive part of the quantized universal enveloping algebra, and Aq(g) be the quantized algebra of functions. We show that the transition matrix of the PBW bases of U⁺q(g) coincides with the intertwiner between the irreducible Aq(g)-mo...