Dunkl operator formalism for quantum many-body problems associated with classical root systems

被引：81
作者：
Hikami, K
机构：
来源：
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN | 1996年 / 65卷 / 02期
关键词：
integrable system; inverse-square interaction; Yang-Baxter equation; reflection equation; root system; Hecke algebra; Dunkl operator; exclusion statistics;
D O I：
10.1143/JPSJ.65.394
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The integrable quantum many-body systems associated with the classical root systems are formulated in terms of the (trigonometric) Dunkl operators. We define the Dunkl operators by use of the infinite-dimensional representation of the R and K matrices for the Yang-Baxter equation and the reflection equation. The eigenvalues of systems are also given.
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页码：394 / 401
页数：8
相关论文
共 42 条
[1]   CRITICAL-THEORY OF OVERSCREENED KONDO FIXED-POINTS [J].
AFFLECK, I ;
LUDWIG, AWW .
NUCLEAR PHYSICS B, 1991, 360 (2-3) :641-696
[2]  
Baxter RJ., 1982, Exactly solved models in statistical mechanics
[3]   YANG-BAXTER EQUATION IN LONG-RANGE INTERACTING SYSTEMS [J].
BERNARD, D ;
GAUDIN, M ;
HALDANE, FDM ;
PASQUIER, V .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (20) :5219-5236
[4]   EXACT SOLUTION OF LONG-RANGE INTERACTING SPIN CHAINS WITH BOUNDARIES [J].
BERNARD, D ;
PASQUIER, V ;
SERBAN, D .
EUROPHYSICS LETTERS, 1995, 30 (05) :301-306
[5]  
BERNARD D, 1995, NEW DEV INTEGRABLE S
[6]   ELLIPTIC DUNKL OPERATORS, ROOT SYSTEMS, AND FUNCTIONAL-EQUATIONS [J].
BUCHSTABER, VM ;
FELDER, G ;
VESELOV, AP .
DUKE MATHEMATICAL JOURNAL, 1994, 76 (03) :885-911
[7]   SOLUTION OF A 3-BODY PROBLEM IN ONE DIMENSION [J].
CALOGERO, F .
JOURNAL OF MATHEMATICAL PHYSICS, 1969, 10 (12) :2191-&
[8]   DEGENERATE AFFINE HECKE ALGEBRAS AND 2-DIMENSIONAL PARTICLES [J].
CHEREDNIK, I .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1992, 7 :109-140
[9]   ELLIPTIC QUANTUM MANY-BODY PROBLEM AND DOUBLE AFFINE KNIZHNIK-ZAMOLODOHIKOV EQUATION [J].
CHEREDNIK, I .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 169 (02) :441-461
[10]   FACTORIZING PARTICLES ON A HALF-LINE AND ROOT SYSTEMS [J].
CHEREDNIK, IV .
THEORETICAL AND MATHEMATICAL PHYSICS, 1984, 61 (01) :977-983
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