Symmetric Functions and 3D Fermion Representation of W1+∞ Algebra

被引：0

作者：

Wang Na ^{[1
]}

Bai Yang ^{[1
]}

Cui Zhennan ^{[1
]}

Wu Ke ^{[2
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng 475001, Peoples R China

[2] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2023年 / 33卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Symmetric functions; 3D Young diagram; Affine Yangian; W1+infinity algebra; Miura transformation;

D O I：

10.1007/s00006-022-01247-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the actions of affine Yangian and W1+infinity algebra on three cases of symmetric functions. The first one is Schur functions of 2D Young diagrams. It is known that affine Yangian and W1+infinity algebra can be represented by 1 Boson field with center 1 in this case. The second case is the symmetric functions Y-lambda(p) of 2D Young diagrams which we defined. They become Jack polynomials when h(1) = h, h(2) = -h(-1). In this case affine Yangian and W1+infinity algebra can be represented by 1 Boson field with center -h(epsilon)/sigma(3). The third case is 3-Jack polynomials of 3D Young diagrams who have at most N layers in z-axis direction. We show that in this case affine Yangian and W1+infinity algebra can be represented by N Boson field with center -h(epsilon)/sigma(3). At each case, we define the Fermions Gamma(m) and Gamma*(m) and use them to represent the W1+infinity algebra.

引用

页数：36