相关论文: Relative braid group symmetries on quantum supersy…

We initiate a general approach to the relative braid group symmetries on (universal) $\imath$quantum groups, arising from quantum symmetric pairs of arbitrary finite types, and their modules. Our approach is built on new intertwining…

We present a comprehensive generalization of Lusztig's braid group symmetries for quasi-split iquantum groups. Specifically, we give 3 explicit rank one formulas for symmetries acting on integrable modules over a quasi-split iquantum group…

Recently, relative braid group actions on $\imath$quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction to $\imath$quantum groups of Kac-Moody type. We formulate…

In the present paper we construct braid group actions on quantum symmetric pair coideal subalgebras of type AIII/AIV. This completes the proof of a conjecture by Kolb and Pellegrini in the case where the underlying Lie algebra is…

The role of quantum groups and braid groups in the description of Standard Model particles is discussed. Some recent results on the use of the quantum group $SU_q(3)$ as a flavour symmetry are reviewed and a connection between two…

We formulate and classify super Satake diagrams under a mild assumption, building on arbitrary Dynkin diagrams for finite-dimensional basic Lie superalgebras. We develop a theory of quantum supersymmetric pairs associated to the super…

This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…

In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…

This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, $\imath$Schur duality, canonical bases, super Kazhdan-Lusztig theory, $\imath$Hall algebras, current presentations…

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…

We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid…

let $\widetilde{\bf U}^\imath$ be a quasi-split universal $\imath$quantum group associated to a quantum symmetric pair $(\widetilde{\bf U}, \widetilde{\bf U}^\imath)$ of Kac-Moody type with a diagram involution $\tau$. We establish the…

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided…

There is a natural action of the braid group on the symmetric matrices with units on the diagonal, appearing in various fields as Singularity Theory, Frobenius Manifolds or Isomonodromic deformations of certain classes of linear…

We establish automorphisms with closed formulas on quasi-split $\imath$quantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of $\imath$Hall algebras and reflection…

We construct quantum supersymmetric pairs $({\bold U},{\bold U}^\imath)$ of type AIII and elucidate their fundamental properties. An $\imath$Schur duality between the $\imath$quantum supergroup ${\bold U}^\imath$ and the Hecke algebra of…

The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras…

We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular coideal subalgebras. Such categories form a prevalent class of braided module categories. This is…

The pair consisting of a quantum group and its corresponding coideal subalgebra, known as a quantum symmetric pair, was developed independently by M. Noumi and G. Letzter through different approaches. The purpose of this paper is threefold.…

The theory of quantum symmetric pairs provides a universal K-matrix which is an analogue of the universal R-matrix for quantum groups. The main ingredient in the construction of the universal K-matrix is a quasi K-matrix which has so far…