Wu, Dongyu
(2021)
The Stable Limit DAHA and the Double Dyck Path Algebra.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
This is the latest version of this item.
Abstract
The double Dyck path algebra (DDPA) is the key algebraic structure that governs the phenomena behind the shuffle and rational shuffle conjectures. The structure emerged from their considerations and computational experiments while attacking the conjecture. Nevertheless, the DDPA bears some resemblance to the structure of a type A double affine Hecke algebra (DAHA). While trying to address this resemblance, Carlsson and Mellit noted one aspect that differentiates the two structures and speculated on how they could be ultimately related. The goal of my thesis is to explain how the DDPA emerges naturally and canonically (as a stable limit) from the family of GLn DAHA's.
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Details
Item Type: |
University of Pittsburgh ETD
|
Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
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Date: |
3 May 2021 |
Date Type: |
Publication |
Defense Date: |
1 April 2021 |
Approval Date: |
3 May 2021 |
Submission Date: |
1 April 2021 |
Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
Number of Pages: |
87 |
Institution: |
University of Pittsburgh |
Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
Degree: |
PhD - Doctor of Philosophy |
Thesis Type: |
Doctoral Dissertation |
Refereed: |
Yes |
Uncontrolled Keywords: |
double affine Hecke algebra, Dyck path, shuffle conjecture, Macdonald polynomial, quantum algebra, representation theory |
Date Deposited: |
03 May 2021 15:14 |
Last Modified: |
03 May 2021 15:14 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/40522 |
Available Versions of this Item
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The Stable Limit DAHA and the Double Dyck Path Algebra. (deposited 03 May 2021 15:14)
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