DAHA and skein algebra of surfaces: double-torus knots

研究成果: ジャーナルへの寄稿記事

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.

元の言語英語
ページ(範囲)2305-2358
ページ数54
ジャーナルLetters in Mathematical Physics
109
発行部数10
DOI
出版物ステータス出版済み - 10 1 2019

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Affine Hecke Algebra
Torus knot
algebra
Algebra
polynomials
Genus
Colored Jones Polynomial
Dehn Twist
Simple Closed Curve
Polynomial
Torus

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

DAHA and skein algebra of surfaces : double-torus knots. / Hikami, Kazuhiro.

:: Letters in Mathematical Physics, 巻 109, 番号 10, 01.10.2019, p. 2305-2358.

研究成果: ジャーナルへの寄稿記事

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