Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)

<Previous Article In Volume
Next Article In Volume>

Branes and Representations of DAHA C∨C1

Authors
Junkang Huang1, *, Satoshi Nawata1, Yutai Zhang1
1Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai, China
*Corresponding author. Email: junkang-huang@outlook.com
Corresponding Author
Junkang Huang
Available Online 17 July 2025.
DOI
10.2991/978-94-6463-789-2_4How to use a DOI?
Keywords
brane quantization; double affine Hecke algebra; topological string theory
Abstract

In this proceeding, we briefly summarize the results of [1], which investigates the representation theory of the spherical double affine Hecke algebra (DAHA) of type C∨C1, using brane quantization. Our analysis establishes a bijective correspondence between compact Lagrangian A-branes in the SL(2,C) character variety of four-punctured spheres and finite-dimensional representations of the spherical DAHA. This correspondence provides evidence for a derived equivalence between two categories: the A-brane category of the character variety and the representation category of the spherical DAHA. The D4 root system plays a central role in understanding both the geometric and representation-theoretic structures underlying this correspondence.

Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Download article (PDF)

<Previous Article In Volume
Next Article In Volume>
Volume Title
Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
Series
Advances in Physics Research
Publication Date
17 July 2025
ISBN
978-94-6463-789-2
ISSN
2352-541X
DOI
10.2991/978-94-6463-789-2_4How to use a DOI?
Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Junkang Huang
AU  - Satoshi Nawata
AU  - Yutai Zhang
PY  - 2025
DA  - 2025/07/17
TI  - Branes and Representations of DAHA C∨C₁
BT  - Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
PB  - Atlantis Press
SP  - 34
EP  - 49
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-789-2_4
DO  - 10.2991/978-94-6463-789-2_4
ID  - Huang2025
ER  -