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Эта публикация цитируется в 12 научных статьях (всего в 12 статьях)
A Common Structure in PBW Bases of the Nilpotent Subalgebra of $U_q(\mathfrak{g})$ and Quantized Algebra of Functions
Atsuo Kunibaa, Masato Okadob, Yasuhiko Yamadac a Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
b Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
c Department of Mathematics, Faculty of Science, Kobe University, Hyogo 657-8501, Japan
Аннотация:
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 $A_q(\mathfrak{g})$.
Ключевые слова:
quantized enveloping algebra; PBW bases; quantized algebra of functions; tetrahedron equation.
Поступила: 19 марта 2013 г.; в окончательном варианте 10 июля 2013 г.; опубликована 19 июля 2013 г.
Образец цитирования:
Atsuo Kuniba, Masato Okado, Yasuhiko Yamada, “A Common Structure in PBW Bases of the Nilpotent Subalgebra of $U_q(\mathfrak{g})$ and Quantized Algebra of Functions”, SIGMA, 9 (2013), 049, 23 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma832 https://www.mathnet.ru/rus/sigma/v9/p49
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