The Stable Limit DAHA and the Double Dyck Path Algebra
Quantum Algebra
2022-09-19 v3 Combinatorics
Representation Theory
Abstract
We study the compatibility of the action of the DAHA of type GL with two inverse systems of polynomial rings obtained from the standard Laurent polynomial representations. In both cases, the crucial analysis is that of the compatibility of the action of the Cherednik operators. Each case leads to a representation of a limit structure (the +/- stable limit DAHA) on a space of almost symmetric polynomials in infinitely many variables (the standard representation). As an application, we show that the defining representation of the double Dyck path algebra arises from the standard representation of the +stable limit DAHA.
Cite
@article{arxiv.2011.12189,
title = {The Stable Limit DAHA and the Double Dyck Path Algebra},
author = {Bogdan Ion and Dongyu Wu},
journal= {arXiv preprint arXiv:2011.12189},
year = {2022}
}
Comments
v1,2: 35pg; v3: 41 pg, expository changes (including an index of notation)