| Autor: |
Na, Wang, Yang, Bai, Zhennan, Cui, Ke, Wu |
| Zdroj: |
Advances in Applied Clifford Algebras; Feb2023, Vol. 33 Issue 1, p1-36, 36p |
| Abstrakt: |
In this paper, we consider the actions of affine Yangian and W 1 + ∞ algebra on three cases of symmetric functions. The first one is Schur functions of 2D Young diagrams. It is known that affine Yangian and W 1 + ∞ algebra can be represented by 1 Boson field with center 1 in this case. The second case is the symmetric functions Y λ (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 W 1 + ∞ algebra can be represented by 1 Boson field with center - h ϵ / σ 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 W 1 + ∞ algebra can be represented by N Boson field with center - h ϵ / σ 3 . At each case, we define the Fermions Γ m and Γ m ∗ and use them to represent the W 1 + ∞ algebra. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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