Hermitian representations of the extended affine Lie algebra over tilde gl2 (Cq)

被引：20

作者：

Gao, Yun ^{[1
]}

Zeng, Ziting ^{[1
]}

机构：

[1] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

ADVANCES IN MATHEMATICS | 2006年 / 207卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

extended affine Lie algebra; quantum torus; hermitian form; highest weight representation;

D O I：

10.1016/j.aim.2005.11.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra gl(2)(C-q) coordinatized by the quantum torus C-q and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：244 / 265

页数：22

共 20 条

[1] A characterization of affine Kac-Moody lie algebras
Allison, BN
Berman, S
Gao, Y
Pianzola, A
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 185 (03) : 671 - 688
[2] Allison BN., 1997, MEM AM MATH SOC, V126, P605
[3] Quantum tori and the structure of elliptic quasi-simple Lie algebras
Berman, S
Gao, Y
Krylyuk, YS
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 135 (02) : 339 - 389
[4] A unified view of some vertex operator constructions
Berman, S
Gao, Y
Tan, SB
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2003, 134 (1) : 29 - 60
[5] Berman S., 1999, CONT MATH, V248, P39
[6] Etingof Pavel I., 1998, MATH SURVEYS MONOGR, V58
[7] FEIGIN BL, 1990, COMMUN MATH PHYS, V128, P161, DOI 10.1007/BF02097051
[8] Representations of extended affine Lie algebras coordinatized by certain quantum tori
Gao, Y
[J]. COMPOSITIO MATHEMATICA, 2000, 123 (01) : 1 - 25
[9] Gao Y, 2000, COMMUN MATH PHYS, V211, P745, DOI 10.1007/s002200050834
[10] Fermionic and bosonic representations of the extended affine Lie algebra gIN(Cq)
Gao, Y
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2002, 45 (04): : 623 - 633

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