Isomorphism between twisted $q$-Yangians and affine $ı$quantum groups: type AI

Abstract

By employing Gauss decomposition, we establish a direct and explicit isomorphism between the twisted $q$-Yangians (in R-matrix presentation) and affine $ı$quantum groups (in current presentation) associated to symmetric pair of type AI introduced by Molev-Ragoucy-Sorba and Lu-Wang, respectively. As a corollary, we obtain a PBW type basis for affine $ı$quantum groups of type AI.

24 pages; v2 fixed typos and updated references

References in corpus (12)

• Quantum symmetric Kac-Moody pairs
• Braid Group Action and Quantum Affine Algebras
• Parabolic presentations of the Yangian Y(gl_n)
• Coideal subalgebras in quantum affine algebras
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: type C
• Twisted Yangians for symmetric pairs of types B, C, D
• Bethe vectors for orthogonal integrable models
• $ı$Hall algebra of the projective line and $q$-Onsager algebra
• PBWD bases and shuffle algebra realizations for $U_v(L{\mathfrak{sl}}_n),U_{v_1,v_2}(L{\mathfrak{sl}}_n),U_v(L\mathfrak{sl}(m|n))$ and their integral forms
• From Twisted Quantum Loop Algebras to Twisted Yangians
• Affine $ı$quantum groups and twisted Yangians in Drinfeld presentations

Cited by in corpus (2)

• Twisted q-Yangians and Sklyanin determinants
• Twisted super Yangians of type AIII and their representations