Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data
Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data
复制标题
所有嘉当数据的 A 型超杨量和量子仿射超代数的洗牌代数实现
DOI：
--
复制
发表时间：
2019
影响因子：
1.2
通讯作者：
A. Tsymbaliuk
中科院分区：
文献类型：
--
作者：
A. Tsymbaliuk
We introduce super Yangians of gl(V),sl(V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {gl}(V),\mathfrak {sl}(V)$$\end{document} (in the new Drinfeld realization) associated with all Dynkin diagrams. We show that all of them are isomorphic to the super Yangians introduced by Nazarov (Lett Math Phys 21(2), 123–131, 1991), by identifying them with the corresponding RTT super Yangians. However, their “positive halves” are not pairwise isomorphic, and we obtain the shuffle algebra realizations for all of those in spirit of Tsymbaliuk (PBWD bases and shuffle algebra realizations for Uv(Lsln),Uv1,v2(Lsln),Uv(Lsl(m|n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{\varvec{v}}(L{\mathfrak {sl}}_n), U_{{\varvec{v}}_1,{\varvec{v}}_2}(L{\mathfrak {sl}}_n), U_{\varvec{v}}(L{\mathfrak {sl}}(m|n))$$\end{document} and their integral forms, preprint, arXiv:1808.09536). We adapt the latter to the trigonometric setup by obtaining the shuffle algebra realizations of the “positive halves” of type A quantum loop superalgebras associated with arbitrary Dynkin diagrams.
We introduce super Yangians of gl(V),sl(V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {gl}(V),\mathfrak {sl}(V)$$\end{document} (in the new Drinfeld realization) associated with all Dynkin diagrams. We show that all of them are isomorphic to the super Yangians introduced by Nazarov (Lett Math Phys 21(2), 123–131, 1991), by identifying them with the corresponding RTT super Yangians. However, their “positive halves” are not pairwise isomorphic, and we obtain the shuffle algebra realizations for all of those in spirit of Tsymbaliuk (PBWD bases and shuffle algebra realizations for Uv(Lsln),Uv1,v2(Lsln),Uv(Lsl(m|n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{\varvec{v}}(L{\mathfrak {sl}}_n), U_{{\varvec{v}}_1,{\varvec{v}}_2}(L{\mathfrak {sl}}_n), U_{\varvec{v}}(L{\mathfrak {sl}}(m|n))$$\end{document} and their integral forms, preprint, arXiv:1808.09536). We adapt the latter to the trigonometric setup by obtaining the shuffle algebra realizations of the “positive halves” of type A quantum loop superalgebras associated with arbitrary Dynkin diagrams.
DOI：
10.1007/s00029-021-00634-5
发表时间：
2018-08
期刊：
Selecta Mathematica
影响因子：
--
作者：
A. Tsymbaliuk
通讯作者：
A. Tsymbaliuk