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The Stable Limit DAHA and the Double Dyck Path Algebra

Wu, Dongyu (2021) The Stable Limit DAHA and the Double Dyck Path Algebra. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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Status: Unpublished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:
CreatorsEmailPitt UsernameORCID
Wu, Dongyudow16@pitt.edu
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIon, Bogdanbion@pitt.edu
Committee MemberFedorov, Romanrmfedorov@gmail.com
Committee MemberHales, Thomashales@pitt.edu
Committee MemberHaglund, Jamesjhaglund@math.upenn.edu
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

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