Murnaghan-Type Representations for the Positive Elliptic Hall Algebra

[2405.00756] Murnaghan-Type Representations for the Positive Elliptic Hall Algebra Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2405.00756 (math) [Submitted on 1 May 2024 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Murnaghan-Type Representations for the Positive Elliptic Hall Algebra Authors: Milo Bechtloff Weising View a PDF of the paper titled Murnaghan-Type Representations for the Positive Elliptic Hall Algebra, by Milo Bechtloff Weising View PDF Abstract: We construct a new family of graded representations $\widetilde{W}_{\lambda}$ for the positive elliptic Hall algebra $\mathcal{E}^{+}$ indexed by Young diagrams $\lambda$ which generalize the standard $\mathcal{E}^{+}$ action on symmetric functions. These representations have homogeneous bases of eigenvectors for the action of the Macdonald element $P_{0,1} \in \mathcal{E}^{+}$ with distinct $\mathbb{Q}(q,t)$-rational spectrum generalizing the symmetric Macdonald functions. The analysis of the structure of these representations exhibits interesting combinatorics arising from the limits of periodic standard Young tableaux. We find an explicit combinatorial rule for the action of the multiplication operators $e_r^{\bullet}$ generalizing the Pieri rule for symmetric Macdonald functions. Comments: This is the complete version of the author's accepted FPSAC24 extended abstract arXiv:2310.10249 Subjects: Combinatorics (math.CO) ; Representation Theory (math.RT) Cite as: arXiv:2405.00756 [math.CO] (or arXiv:2405.00756v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2405.00756 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SIGMA 22 (2026), 076, 50 pages Related DOI : https://doi.org/10.3842/SIGMA.2026.076 Focus to learn more DOI(s) linking to related resources Submission history From: Milo Bechtloff Weising [ view email ] [via Journal Sigma as proxy] [v1] Wed, 1 May 2024 08:31:03 UTC (48 KB) [v2] Fri, 14 Aug 2026 20:18:09 UTC (48 KB) Full-text links: Access Paper: View a PDF of the paper titled Murnaghan-Type Representations for the Positive Elliptic Hall Algebra, by Milo Bechtloff Weising View PDF TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-05 Change to browse by: math math.RT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Computations of Cohomology of Arithmetic Groups, Part 1#1076525
• Rook characters as symmetric functions#986651
• Perturbative anomalies in quantum mechanics#799963
• On the nonexistence of good involutions on symplectic quandles#1129232
• The commutator subalgebra of the Lie algebra associated with a right-angled Coxeter group#1105904