RLL-REALIZATION OF TWO-PARAMETER QUANTUM AFFINE ALGEBRA IN TYPE Dn(1)

Rushu Zhuang; Naihong Hu; Xiao Xu

doi:10.2140/pjm.2024.329.357

RLL-REALIZATION OF TWO-PARAMETER QUANTUM AFFINE ALGEBRA IN TYPE D_n⁽¹⁾

Rushu Zhuang, Naihong Hu, Xiao Xu

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We obtain the basic R-matrix of the two-parameter quantum group U = U_{r, s}(so_2n) via its weight representation theory and determine its R-matrix with spectral parameters for the two-parameter quantum affine algebra U = U_{r, s}(so d_2n). Using the Gauss decomposition of the R-matrix realization of U = U_{r, s}(so_2n), we study the commutation relations of the Gaussian generators and finally arrive at its RLL-formalism of the Drinfeld realization of two-parameter quantum affine algebra U = U_{r, s}(so d_2n).

Original language	English
Pages (from-to)	357-395
Number of pages	39
Journal	Pacific Journal of Mathematics
Volume	329
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2024.329.357
State	Published - 2024

Keywords

Drinfeld realization
Gauss decomposition
RLL formulation
basic R-matrix
quantum affine algebra

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title = "RLL-REALIZATION OF TWO-PARAMETER QUANTUM AFFINE ALGEBRA IN TYPE Dn(1)",

abstract = "We obtain the basic R-matrix of the two-parameter quantum group U = Ur, s(so2n) via its weight representation theory and determine its R-matrix with spectral parameters for the two-parameter quantum affine algebra U = Ur, s(so d2n). Using the Gauss decomposition of the R-matrix realization of U = Ur, s(so2n), we study the commutation relations of the Gaussian generators and finally arrive at its RLL-formalism of the Drinfeld realization of two-parameter quantum affine algebra U = Ur, s(so d2n).",

keywords = "Drinfeld realization, Gauss decomposition, RLL formulation, basic R-matrix, quantum affine algebra",

author = "Rushu Zhuang and Naihong Hu and Xiao Xu",

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AU - Zhuang, Rushu

AU - Hu, Naihong

AU - Xu, Xiao

N1 - Publisher Copyright: © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

PY - 2024

Y1 - 2024

N2 - We obtain the basic R-matrix of the two-parameter quantum group U = Ur, s(so2n) via its weight representation theory and determine its R-matrix with spectral parameters for the two-parameter quantum affine algebra U = Ur, s(so d2n). Using the Gauss decomposition of the R-matrix realization of U = Ur, s(so2n), we study the commutation relations of the Gaussian generators and finally arrive at its RLL-formalism of the Drinfeld realization of two-parameter quantum affine algebra U = Ur, s(so d2n).

AB - We obtain the basic R-matrix of the two-parameter quantum group U = Ur, s(so2n) via its weight representation theory and determine its R-matrix with spectral parameters for the two-parameter quantum affine algebra U = Ur, s(so d2n). Using the Gauss decomposition of the R-matrix realization of U = Ur, s(so2n), we study the commutation relations of the Gaussian generators and finally arrive at its RLL-formalism of the Drinfeld realization of two-parameter quantum affine algebra U = Ur, s(so d2n).

KW - Drinfeld realization

KW - Gauss decomposition

KW - RLL formulation

KW - basic R-matrix

KW - quantum affine algebra

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U2 - 10.2140/pjm.2024.329.357

DO - 10.2140/pjm.2024.329.357

M3 - 文章

AN - SCOPUS:85199411166

SN - 0030-8730

VL - 329

SP - 357

EP - 395

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

RLL-REALIZATION OF TWO-PARAMETER QUANTUM AFFINE ALGEBRA IN TYPE D_n⁽¹⁾

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