A Drinfeld type presentation of twisted Yangians of quasi-split type

K Lu, W Zhang - arXiv preprint arXiv:2408.06981, 2024 - arxiv.org
We formulate a family of algebras, twisted Yangians (of simply-laced quasi-split type) in
Drinfeld type current generators and defining relations. These new algebras admit PBW type …

Braid Group Action and Quasi-Split Affine Quantum Groups II: Higher Rank

M Lu, W Wang, W Zhang - Communications in Mathematical Physics, 2024 - Springer
This paper studies quantum symmetric pairs (U~, U~ ı) associated with quasi-split Satake
diagrams of affine type A 2 r-1, D r, E 6 with a nontrivial diagram involution fixing the affine …

Relative braid group symmetries on quantum groups of Kac–Moody type

W Zhang - Selecta Mathematica, 2023 - Springer
Recently, relative braid group symmetries on ı quantum groups of arbitrary finite types have
been constructed by Wang and the author. In this paper, generalizing that finite-type …

Boundary transfer matrices arising from quantum symmetric pairs

A Appel, B Vlaar - arXiv preprint arXiv:2410.21654, 2024 - arxiv.org
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's
two-row transfer matrix approach for quantum integrable systems with boundary conditions …

Finite Young wall model for representations of quantum group

S Han - Journal of Algebraic Combinatorics, 2024 - Springer
Finite Young wall model for representations of $$\imath $$ quantum group $${\textbf{U}}^{\jmath
}$$ | Journal of Algebraic Combinatorics Skip to main content SpringerLink Account Menu …

Differential operator realization of braid group action on ıquantum groups

Z Fan, J Geng, S Han - Journal of Mathematical Physics, 2023 - pubs.aip.org
We construct a unique braid group action on deformed q-Weyl algebra A q (S)⁠. Under this
action, we give a realization of the braid group action on quasi-split ıquantum groups U (S) ı …

Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs

T Przezdziecki - arXiv preprint arXiv:2311.13705, 2023 - arxiv.org
We formulate a precise connection between the new Drinfeld presentation of a quantum
affine algebra $ U_q\widehat {\mathfrak {g}} $ and the new Drinfeld presentation of affine …

Braid group action and quasi-split affine quantum groups II: higher rank

M Lu, W Wang, W Zhang - arXiv preprint arXiv:2311.10299, 2023 - arxiv.org
This paper studies quantum symmetric pairs $(\widetilde {\mathbf U},\widetilde {{\mathbf
U}}^\imath) $ associated with quasi-split Satake diagrams of affine type $ A_ {2r-1}, D_r, E …

Affine quantum groups and Steinberg varieties of type C

C Su, W Wang - arXiv preprint arXiv:2407.06865, 2024 - arxiv.org
We provide a geometric realization of the quasi-split affine $\imath $ quantum group of type
AIII $ _ {2n-1}^{(\tau)} $ in terms of equivariant K-groups of non-connected Steinberg …

Differential operator realization of braid group action on quantum groups

Z Fan, J Geng, S Han - arXiv preprint arXiv:2307.03501, 2023 - arxiv.org
We construct a unique braid group action on modified $ q $-Weyl algebra $\mathbf A_q (S)
$. Under this action, we give a realization of the braid group action on quasi-split $\imath …