DAHA and skein algebra of surfaces: double-torus knots

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

We study a topological aspect of rank-1 double-affine Hecke algebra (DAHA). Clarified is a relationship between the DAHA of A1-type (resp. CC1-type) and the skein algebra on a once-punctured torus (resp. a 4-punctured sphere), and the SL(2 ; Z) actions of DAHAs are identified with the Dehn twists on the surfaces. Combining these two types of DAHA, we construct the DAHA representation for the skein algebra on a genus-two surface, and we propose a DAHA polynomial for a double-torus knot, which is a simple closed curve on a genus-two Heegaard surface in S3. Discussed is a relationship between the DAHA polynomial and the colored Jones polynomial.

本文言語英語
ページ(範囲)2305-2358
ページ数54
ジャーナルLetters in Mathematical Physics
109
10
DOI
出版ステータス出版済み - 10 1 2019

All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 数理物理学

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