☆ 4.0 Article

Braid group action and quasi-split affine ?quantum groups I

Representation Theory (2023)

Related references

Note: Only part of the references are listed.

Article Mathematics

An intrinsic approach to relative braid group symmetries on ıquantum groups

Weiqiang Wang et al.

Summary: This paper introduces the application of relative braid groups on quantum symmetric pairs and establishes some fundamental properties corresponding to quantum groups. The study also shows how to verify the relative braid relations by constructing rank one factorizations of quasi K-matrices, and applies these symmetries to the construction of compatible relative braid group actions on modules over quantum groups.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY (2023)

Add to Collection

Article Mathematics

Hall algebras and quantum symmetric pairs I: Foundations

Ming Lu et al.

Summary: This study investigates the categorification of quantum symmetric pairs and introduces a Hall algebra approach to address this issue. A universal quantum group (U-iota) tilde is introduced and <(U-sigma(iota))tilde> is recovered through central reduction. Additionally, the scope of Ringel-Hall algebras is extended, and a new class of 1-Gorenstein algebras based on quiver algebras is introduced.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY (2022)

Add to Collection

Article Mathematics

HALL ALGEBRA OF THE PROJECTIVE LINE AND q-ONSAGER ALGEBRA

M. I. N. G. Lu et al.

Summary: This article studies the iHall algebra on the projective line and shows that it realizes the universal q-Onsager algebra. It also establishes a derived equivalence between the iHall algebras of the projective line and the Kronecker quiver, explaining the isomorphism of the q-Onsager algebra under two different presentations.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2022)

Add to Collection

Article Physics, Mathematical

A Drinfeld-type presentation of affine/quantum groups II: split BCFG type

Weinan Zhang

Summary: In this paper, we generalize the Drinfeld-type presentation of Lu and Wang for the split affine ADE type of (U) over tilde (iota) to arbitrary split affine types of (U) over tilde (iota).

LETTERS IN MATHEMATICAL PHYSICS (2022)

Add to Collection

Article Mathematics, Applied

Braid group symmetries on quasi-split ι quantum groups via ι Hall algebras

Ming Lu et al.

Summary: We establish automorphisms with closed formulas on quasi-split iota quantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of iota Hall algebras and reflection functors, and several quantum binomial identities arising along the way are established.

SELECTA MATHEMATICA-NEW SERIES (2022)

Add to Collection

Article Mathematics

A SERRE PRESENTATION FOR THEQUANTUM GROUPS

Xinhong Chen et al.

Summary: For a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, the group is presented with explicit relations, and the verification of new relations is simplified to new q-binomial identities. It is shown that, under suitable conditions on the parameters, the group admits a bar involution.

TRANSFORMATION GROUPS (2021)

Add to Collection

Article Mathematics

A Drinfeld type presentation of affine iquantum groups I: Split ADE type

Ming Lu et al.

Summary: The study introduces a new Drinfeld-type presentation for iquantum groups arising from quantum symmetric pairs of split affine ADE type, with the q-Onsager algebra included as a special case. This presentation can be seen as a deformation of half an affine quantum group in the Drinfeld presentation.

ADVANCES IN MATHEMATICS (2021)

Add to Collection

Article Physics, Mathematical

Hall Algebras and Quantum Symmetric Pairs II: Reflection Functors

Ming Lu et al.

Summary: By using BGP type reflection functors, the authors construct and study iHall algebras, leading to a conceptual construction of q-root vectors and PBW bases for (universal) quasi-split iquantum groups of ADE type. The symmetries on iHall algebras for Dynkin quivers induce automorphisms of universal iquantum groups that satisfy the braid group relations associated to the restricted Weyl group of a symmetric pair.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2021)

Add to Collection

Article Mathematics

BRAID GROUP ACTION AND ROOT VECTORS FOR THE q-ONSAGER ALGEBRA

Pascal Baseilhac et al.

TRANSFORMATION GROUPS (2020)

Add to Collection

Article Mathematics

Affine flag varieties and quantum symmetric pairs

Z. Fan et al.

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY (2020)

Add to Collection

Article Mathematics, Applied

Factorisation of quasi K-matrices for quantum symmetric pairs

Liam Dobson et al.

SELECTA MATHEMATICA-NEW SERIES (2019)

Add to Collection

Article Mathematics

The Lusztig automorphism of the q-Onsager algebra

Paul Terwilliger

JOURNAL OF ALGEBRA (2018)

Add to Collection

Article Mathematics

From the Drinfeld Realization to the Drinfeld-Jimbo Presentation of Affine Quantum Algebras: Injectivity

Ilaria Damiani

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES (2015)

Add to Collection

Article Mathematics

Quantum symmetric Kac-Moody pairs

Stefan Kolb

ADVANCES IN MATHEMATICS (2014)

Add to Collection

Article Mathematics

Braid group actions on coideal subalgebras of quantized enveloping algebras

Stefan Kolb et al.

JOURNAL OF ALGEBRA (2011)

Add to Collection

Article Physics, Mathematical

Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories

Pascal Baseilhac et al.

LETTERS IN MATHEMATICAL PHYSICS (2010)

Add to Collection

Article Physics, Particles & Fields

A new (in)finite-dimensional algebra for quantum integrable models

P Baseilhac et al.

NUCLEAR PHYSICS B (2005)

Add to Collection

Article Physics, Mathematical

Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras

E Frenkel et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2001)

Add to Collection

© Peeref 2019-2024. All rights reserved.