Congruence Skein Relations for Colored HOMFLY-PT Invariants

被引：0

作者：

Chen, Qingtao ^{[1
]}

Liu, Kefeng ^{[2
,3
]}

Peng, Pan ^{[4
]}

Zhu, Shengmao ^{[5
]}

机构：

[1] New York Univ Abu Dhabi, Div Sci, Abu Dhabi, U Arab Emirates

[2] Chongqing Univ Technol, Math Sci Res Ctr, Chongqing, Peoples R China

[3] Univ Calif Los Angeles, Dept Math, Box 951555, Los Angeles, CA 90095 USA

[4] Univ Arizona, Dept Math, 617 N St Rita Ave, Tucson, AZ 85721 USA

[5] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 400卷 / 02期

基金：

瑞士国家科学基金会; 美国国家科学基金会;

关键词：

HECKE ALGEBRAS; LINK; KNOT; INTEGRALITY; MODULE;

D O I：

10.1007/s00220-022-04604-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The original HOMFLY-PT polynomials can be fully determined by a very simple rule, the skein relation, while the colored HOMFLY-PT invariants (2 variables) of links are notoriously hard to compute. Inspired by the large N duality connecting Chern-Simons gauge theory and topological string theory, the Labastida-Marino-Ooguri-Vafa (LMOV) conjecture for links (or framed links) predicts integrality, pole order structure and symmetric property for the colored HOMFLY-PT invariants. By studying the LMOV conjecture for framed links, we uncover certain congruence skein relations for the (reformulated) colored HOMFLY-PT invariants. Although these congruence skein relations still can not fully determine the colored HOMFLY-PT invariants, they provide a strong pattern for the colored HOMFLY-PT invariants, which possibly could pave a way for people to understand the very mysterious nature of the colored HOMFLY-PT invariants. We prove that these congruence skein relations hold in many different situations. Finally, we discuss the applications of the congruence skein relations in framed LMOV conjecture.

引用

页码：683 / 729

页数：47

共 40 条

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