Matching realization of Uq(sln+1) of higher rank in the quantum Weyl algebra Wq(2n)

Nai Hong Hu; Shen You Wang

doi:10.1007/s10114-014-3721-3

Matching realization of U_q(sl_n+1) of higher rank in the quantum Weyl algebra W_q(2n)

Nai Hong Hu
, Shen You Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

Abstract

In the paper, we further realize the higher rank quantized universal enveloping algebra U_q(sl_n+1) as certain quantum differential operators in the quantum Weyl algebra W_q(2n) defined over the quantum divided power algebra A_q(n) of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of U_q(sl_n+1). The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.

Original language	English
Pages (from-to)	1674-1688
Number of pages	15
Journal	Acta Mathematica Sinica, English Series
Volume	30
Issue number	10
DOIs	https://doi.org/10.1007/s10114-014-3721-3
State	Published - 1 Sep 2014

Keywords

Lusztig symmetries
Quantum divided power algebra
matching realization
quantum Weyl algebra
quantum differential operators

Access to Document

10.1007/s10114-014-3721-3

Cite this

@article{5fd28a1aeb65450bb90ccd0752e33b02,

title = "Matching realization of Uq(sln+1) of higher rank in the quantum Weyl algebra Wq(2n)",

abstract = "In the paper, we further realize the higher rank quantized universal enveloping algebra Uq(sln+1) as certain quantum differential operators in the quantum Weyl algebra Wq(2n) defined over the quantum divided power algebra Aq(n) of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq(sln+1). The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.",

keywords = "Lusztig symmetries, Quantum divided power algebra, matching realization, quantum Weyl algebra, quantum differential operators",

author = "Hu, \{Nai Hong\} and Wang, \{Shen You\}",

note = "Publisher Copyright: {\textcopyright} 2014, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = sep,

day = "1",

doi = "10.1007/s10114-014-3721-3",

language = "英语",

volume = "30",

pages = "1674--1688",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "10",

}

TY - JOUR

T1 - Matching realization of Uq(sln+1) of higher rank in the quantum Weyl algebra Wq(2n)

AU - Hu, Nai Hong

AU - Wang, Shen You

PY - 2014/9/1

Y1 - 2014/9/1

N2 - In the paper, we further realize the higher rank quantized universal enveloping algebra Uq(sln+1) as certain quantum differential operators in the quantum Weyl algebra Wq(2n) defined over the quantum divided power algebra Aq(n) of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq(sln+1). The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.

AB - In the paper, we further realize the higher rank quantized universal enveloping algebra Uq(sln+1) as certain quantum differential operators in the quantum Weyl algebra Wq(2n) defined over the quantum divided power algebra Aq(n) of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq(sln+1). The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.

KW - Lusztig symmetries

KW - Quantum divided power algebra

KW - matching realization

KW - quantum Weyl algebra

KW - quantum differential operators

UR - https://www.scopus.com/pages/publications/84907659528

U2 - 10.1007/s10114-014-3721-3

DO - 10.1007/s10114-014-3721-3

M3 - 文章

AN - SCOPUS:84907659528

SN - 1439-8516

VL - 30

SP - 1674

EP - 1688

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 10

ER -

Matching realization of U_q(sl_n+1) of higher rank in the quantum Weyl algebra W_q(2n)

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this