VERTEX REPRESENTATIONS FOR YANGIANS OF KAC-MOODY ALGEBRAS

被引：7

作者：

Guay, Nicolas ^{[1
]}

Regelskis, Vidas ^{[2
,3
]}

Wendlandt, Curtis ^{[1
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[3] Vilnius Univ, Inst Theoret Phys & Astron, Sauletekio Av 3, LT-10257 Vilnius, Lithuania

来源：

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES | 2019年 / 6卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Yangian; vertex operator; Kac-Moody algebra; Fock space; twisted group algebra; central extension; LEVEL ONE REPRESENTATIONS; LIE-ALGEBRAS; AFFINE; EXTENSION; OPERATORS;

D O I：

10.5802/jep.103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the Poincare-Birkhoff-Witt property for simply laced affine Yangians.

引用

页码：665 / 706

页数：42

共 42 条

[1]

Appel A., 2019, ARXIV171203601

[2] On the R-matrix realization of Yangians and their representations [J].

Arnaudon, Daniel ;

Molev, Alexander ;

Ragoucy, Eric .

ANNALES HENRI POINCARE, 2006, 7 (7-8) :1269-1325

[3] VERTEX OPERATOR REPRESENTATIONS OF THE QUANTUM AFFINE ALGEBRA UG(BR(1)) [J].

BERNARD, D .

LETTERS IN MATHEMATICAL PHYSICS, 1989, 17 (03) :239-245

[4] LEVEL ONE REPRESENTATIONS OF THE SIMPLE AFFINE KAC-MOODY ALGEBRAS IN THEIR HOMOGENEOUS GRADATIONS [J].

BERNARD, D ;

THIERRYMIEG, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1987, 111 (02) :181-246

[5] Homomorphisms between different quantum toroidal and affine Yangian algebras [J].

Bershtein, Mikhail ;

Tsymbaliuk, Alexander .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (02) :867-899

[6]

Chari W, 2001, DUKE MATH J, V108, P183

[7] Weyl group extension of quantized current algebras [J].

Ding, J ;

Khoroshkin, S .

TRANSFORMATION GROUPS, 2000, 5 (01) :35-59

[8] DEGENERATE AFFINE HECKE ALGEBRAS AND YANGIANS [J].

DRINFELD, VG .

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1986, 20 (01) :58-60

[9]

Finkelberg M., 2019, ARNOLD MATH J

[10]

Frenkel I., 1988, VERTEX OPERATOR ALGE

← 1 2 3 4 5 →