| Autor: |
Atsuo Kuniba, Masato Okado, Yasuhiko Yamada |
| Jazyk: |
angličtina |
| Rok vydání: |
2013 |
| Předmět: |
|
| Zdroj: |
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 049 (2013) |
| Druh dokumentu: |
article |
| ISSN: |
1815-0659 |
| DOI: |
10.3842/SIGMA.2013.049 |
| Popis: |
For a finite-dimensional simple Lie algebra $mathfrak{g}$, let $U^+_q(mathfrak{g})$ be the positive part of the quantized universal enveloping algebra, and $A_q(mathfrak{g})$ be the quantized algebra of functions. We show that the transition matrix of the PBW bases of $U^+_q(mathfrak{g})$ coincides with the intertwiner between the irreducible $A_q(mathfrak{g})$-modules labeled by two different reduced expressions of the longest element of the Weyl group of $mathfrak{g}$. This generalizes the earlier result by Sergeev on $A_2$ related to the tetrahedron equation and endows a new representation theoretical interpretation with the recent solution to the 3D reflection equation for $C_2$. Our proof is based on a realization of $U^+_q(mathfrak{g})$ in a quotient ring of $A_q(mathfrak{g})$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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