DAHA and skein algebra of surfaces: double-torus knots

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)2305-2358
Number of pages54
JournalLetters in Mathematical Physics
Volume109
Issue number10
DOIs
Publication statusPublished - Oct 1 2019

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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